SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                  -----------


                    Under the Securities Exchange Act of 1934

                                  SCHEDULE 13G

                                 AMENDMENT NO.1

             INFORMATION STATEMENT PURSUANT TO RULES 13d-1 AND 13d-2
                    UNDER THE SECURITIES EXCHANGE ACT OF 1934




                       Network-1 Security Solutions, Inc.
                       ----------------------------------
                                (Name of Issuer)



                     Common Stock, par value $0.01 per share
                     ---------------------------------------
                         (Title of Class of Securities)



                                   64121N-10-9
                                   -----------
                                 (CUSIP Number)



                                December 31, 2005
               --------------------------------------------------
             (Date of Event Which Requires Filing of this Statement)



Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

      |_|  Rule 13d-1(b)
      |X|  Rule 13d-1(c)
      |_|  Rule 13d-1(d)

                                   ---------

                                  Page 1 of 12



                                  SCHEDULE 13G

CUSIP No. 98975L108
--------------------------------------------------------------------------------

1)     NAME OF REPORTING PERSON
       S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

       First New York Securities L.L.C.
--------------------------------------------------------------------------------
2)     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP          (a) |_|
                                                                 (b) |x|
--------------------------------------------------------------------------------
3)     SEC USE ONLY

--------------------------------------------------------------------------------
4)     CITIZENSHIP OR PLACE OF ORGANIZATION

       New York
--------------------------------------------------------------------------------
                             5)     SOLE VOTING POWER

       NUMBER                       905,410
       OF                  -----------------------------------------------------
       SHARES                6)     SHARED VOTING POWER
       BENEFICIALLY
       OWNED BY                     0
       EACH                -----------------------------------------------------
       REPORTING             7)     SOLE DISPOSITIVE POWER
       PERSON
       WITH                         905,410
                           -----------------------------------------------------
                             8)     SHARED DISPOSITIVE POWER

                                    0
--------------------------------------------------------------------------------
9)     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

       905,410
--------------------------------------------------------------------------------
10)    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
                                                                   |_|
--------------------------------------------------------------------------------
11)    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

       5.1%
--------------------------------------------------------------------------------
12)    TYPE OF REPORTING PERSON

       BD
--------------------------------------------------------------------------------


                                     2 of 12



                                  SCHEDULE 13G

CUSIP No. 98975L108
--------------------------------------------------------------------------------

1)     NAME OF REPORTING PERSON
       S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

       Steven Heinemann
--------------------------------------------------------------------------------
2)     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP          (a) |_|
                                                                 (b) |x|
--------------------------------------------------------------------------------
3)     SEC USE ONLY

--------------------------------------------------------------------------------
4)     CITIZENSHIP OR PLACE OF ORGANIZATION

       United States
--------------------------------------------------------------------------------
                             5)     SOLE VOTING POWER

       NUMBER                       361,100
       OF                 ------------------------------------------------------
       SHARES                6)     SHARED VOTING POWER
       BENEFICIALLY
       OWNED BY                     0
       EACH               ------------------------------------------------------
       REPORTING             7)     SOLE DISPOSITIVE POWER
       PERSON
       WITH                         361,100
                         -------------------------------------------------------
                             8)     SHARED DISPOSITIVE POWER

                                    540,410
--------------------------------------------------------------------------------
9)     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

       901,510
--------------------------------------------------------------------------------
10)    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
                                                                   |_|
--------------------------------------------------------------------------------
11)    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

       5.0%
--------------------------------------------------------------------------------
12)    TYPE OF REPORTING PERSON

       IN
--------------------------------------------------------------------------------


                                     3 of 12



                                  SCHEDULE 13G

CUSIP No. 98975L108
--------------------------------------------------------------------------------

1)     NAME OF REPORTING PERSON
       S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

       Doug Lipton
--------------------------------------------------------------------------------
2)     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP          (a) |_|
                                                                 (b) |x|
--------------------------------------------------------------------------------
3)     SEC USE ONLY

--------------------------------------------------------------------------------
4)     CITIZENSHIP OR PLACE OF ORGANIZATION

       United States
--------------------------------------------------------------------------------
                               5)     SOLE VOTING POWER

       NUMBER                         146,200
       OF                   ----------------------------------------------------
       SHARES                  6)     SHARED VOTING POWER
       BENEFICIALLY
       OWNED BY                       0
       EACH                 ----------------------------------------------------
       REPORTING               7)     SOLE DISPOSITIVE POWER
       PERSON
       WITH                           146,200
                            ----------------------------------------------------
                               8)     SHARED DISPOSITIVE POWER

                                      540,410
--------------------------------------------------------------------------------
9)     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

       686,610
--------------------------------------------------------------------------------
10)    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
                                                                   |_|
--------------------------------------------------------------------------------
11)    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

       3.9%
--------------------------------------------------------------------------------
12)    TYPE OF REPORTING PERSON

       IN
--------------------------------------------------------------------------------


                                     4 of 12



                                  SCHEDULE 13G

CUSIP No. 98975L108
--------------------------------------------------------------------------------

1)     NAME OF REPORTING PERSON
       S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

       Jay Goldstein
--------------------------------------------------------------------------------
2)     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP          (a) |_|
                                                                 (b) |x|
--------------------------------------------------------------------------------
3)     SEC USE ONLY

--------------------------------------------------------------------------------
4)     CITIZENSHIP OR PLACE OF ORGANIZATION

       United States
--------------------------------------------------------------------------------
                               5)     SOLE VOTING POWER

       NUMBER                         96,500
       OF                   ----------------------------------------------------
       SHARES                  6)     SHARED VOTING POWER
       BENEFICIALLY
       OWNED BY                       0
       EACH                 ----------------------------------------------------
       REPORTING               7)     SOLE DISPOSITIVE POWER
       PERSON
       WITH                           96,500
                            ----------------------------------------------------
                               8)     SHARED DISPOSITIVE POWER

                                      359,000
--------------------------------------------------------------------------------
9)     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

       455,500
--------------------------------------------------------------------------------
10)    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
                                                                   |_|
--------------------------------------------------------------------------------
11)    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

       2.6%
--------------------------------------------------------------------------------
12)    TYPE OF REPORTING PERSON

       BD
--------------------------------------------------------------------------------


                                     5 of 12



                                  Schedule 13G
                                  ------------

Item 1(a).  Name of Issuer:

Network-1 Security Solutions, Inc.

Item 1(b).  Address of Issuer's Principal Executive Offices:

445 Park Avenue, Suite 1028
New York, New York  10022

Item 2(a).  Name of Person Filing:

(1)   First New York Securities L.L.C. ("FNYS")

(2)   Steven Heinemann.   Mr. Heinemann is a Managing Member of FNYS.

(3)   Doug Lipton.        Mr. Lipton is a Member of FNYS.

(4)   Jay Goldstein.      Mr. Goldstein is a Member of FNYS.

Item 2(b).  Address of Principal Business Office or, if None, Residence:

(1)   First New York Securities L.L.C.  850 Third Avenue, 17th Floor
                                        New York, NY  10022

(2)   Steven Heinemann                  c/o First New York Securities L.L.C.
                                        850 Third Avenue, 8th Floor
                                        New York, NY  10022

(3)   Doug Lipton                       c/o First New York Securities L.L.C.
                                        850 Third Avenue, 8th Floor
                                        New York, NY  10022

(4)   Jay Goldstein                     c/o First New York Securities L.L.C.
                                        850 Third Avenue, 8th Floor
                                        New York, NY 10022


                                     6 of 12



Item 2(c).  Citizenship:

(1)   First New York Securities L.L.C.   New York

(2)   Steven Heinemann                   United States

(3)   Doug Lipton                        United States

(4)   Jay Goldstein                      United States

Item 2(d).  Title of Class of Securities:

Common Stock, par value $.01 per share

Item 2(e).  CUSIP Number:

64121N-10-9

Item 3.     If this statement is filed pursuant to ss.ss. 240.13d-1(b), or
            240.13d-2(b) or (c), check whether the person filing is a:

            (a)   |_|   Broker or Dealer Registered Under Section 15 of the Act
                        (15 U.S.C. 78o)

            (b)   |_|   Bank as defined in section 3(a)(6) of the Act (15 U.S.C.
                        78c)

            (c)   |_|   Insurance Company as defined in section 3(a)(19) of the
                        Act (15 U.S.C. 78c)

            (d)   |_|   Investment Company registered under section 8 of the
                        Investment Company Act of 1940 (15 U.S.C. 80a-8)

            (e)   |_|   Investment Adviser in accordance with ss.
                        240.13d-1(b)(1)(ii)(E)

            (f)   |_|   Employee benefit plan or endowment fund in accordance
                        with ss. 240.13d-1(b)(1)(ii)(F)

            (g)   |_|   Parent Holding Company or control person in accordance
                        with ss.240.13d-1(b)(ii)(G)

            (h)   |_|   Savings Association as defined in ss.3(b) of the Federal
                        Deposit Insurance Act (12 U.S.C. 1813)

            (i)   |_|   Church plan that is excluded from the definition of an
                        investment company under ss.3(c)(15) of the Investment
                        Company Act of 1940 (15 U.S.C. 80a-3)

            (j)   |_|   Group, in accordance with ss.240.13d-1(b)(ii)(J)



                                     7 of 12



Item 4.     Ownership.

            (a)         Amount beneficially owned:

                        (1)   First New York Securities L.L.C.    905,410

                        (2)   Steven Heinemann                    901,510(1)

                        (3)   Doug Lipton                         686,610(2)

                        (4)   Jay Goldstein                        455,500

            (b)         Percent of class: (3)

                        (1)   First New York Securities L.L.C.    5.1%

                        (2)   Steven Heinemann                    5.0%

                        (3)   Doug Lipton                         3.9%

                        (4)   Jay Goldstein                       2.6%

            (c)         Number of shares as to which such person has:

                  (i)   Sole power to vote or to direct the vote:

                        (1)   First New York Securities L.L.C.    905,410

                        (2)   Steven Heinemann                    186,100

                        (3)   Doug Lipton                         146,200

                        (4)   Jay Goldstein                        96,500


-----------------------
(1) Includes 100,000 restricted shares and 75,000 warrants.

(2) Includes shares held by Lucia Marie Smith (Doug Lipton's wife).

(3) Percentages are based on 17,697,572 shares of Common Stock outstanding (as
set forth on the Issuer's Form 10-KSB/A, filed on November 23, 2005 with the
Securities and Exchange Commission).


                                     8 of 12



                  (ii)  Shared power to vote or to direct the vote:

                        (1)   First New York Securities L.L.C.    0

                        (2)   Steven Heinemann                    0

                        (3)   Doug Lipton                         0

                        (4)   Jay Goldstein                       0

                  (iii) Sole power to dispose or to direct the disposition of:

                        (1)   First New York Securities L.L.C.    905,410

                        (2)   Steven Heinemann                    186,100

                        (3)   Doug Lipton                         146,200

                        (4)   Jay Goldstein                        96,500

                  (iv)  Shared power to dispose or to direct the disposition of:

                        (1)   First New York Securities L.L.C.    0

                        (2)   Steven Heinemann                    540,410(4)

                        (3)   Doug Lipton                         540,410(4)

                        (4)   Jay Goldstein                       359,000(4)

Item 5.     Ownership of Five Percent or Less of a Class.

Not Applicable.


(4) Includes shares owned by First New York Securities L.L.C. as to which the
    reporting person may be deemed to share dispositive power.

                                     9 of 12



Item 6.     Ownership of More than Five Percent on Behalf of Another Person.

Not Applicable.

Item 7.     Identification and Classification of the Subsidiary Which Acquired
            the Security Being Reported on by the Parent Holding Company.

Not Applicable.

Item 8.     Identification and Classification of Members of the Group.

Not Applicable.

Item 9.     Notice of Dissolution of Group.

Not Applicable.

Item 10.    Certification.

            By signing below I certify that, to the best of my knowledge and
belief, the securities referred to above were acquired and are held in the
ordinary course of business and were not acquired and are not held for the
purpose of or with the effect of changing or influencing the control of the
issuer of the securities and were not acquired and are not held in connection
with or as a participant in any transaction having that purpose or effect.




                                    10 of 12


                                    SIGNATURE
                                    ---------


            After reasonable inquiry and to the best knowledge and belief of the
undersigned, the undersigned certifies that the information set forth in this
statement is true, complete and correct.


Date: February 14, 2006             FIRST NEW YORK SECURITIES L.L.C.

                                    By: /s/ Mario Maugeri
                                        ------------------------------
                                        Name: Mario Maugeri
                                        Title: Director of Operations


                                    /s/ Steven Heinemann
                                    ----------------------------------
                                    Steven Heinemann


                                    /s/ Doug Lipton
                                    ----------------------------------
                                    Doug Lipton


                                    /s/ Jay Goldstein
                                    ----------------------------------
                                    Jay Goldstein



                                    11 of 12




                                                                       Exhibit 1

                            AGREEMENT OF JOINT FILING


      Pursuant to rule 13d-1(k) promulgated under the Securities Exchange Act of
1934, as amended, the undersigned persons hereby agree to file with the
Securities and Exchange Commission the Statement on Schedule 13G (the
"Statement") to which this Agreement is attached as an exhibit, and agree that
such Statement, as so filed is on the behalf of each of them.

      IN WITNESS WHEREOF, the undersigned have executed this Agreement as of
February 14, 2006.

                                    FIRST NEW YORK SECURITIES L.L.C.

                                    By: /s/ Mario Maugeri
                                        -----------------------------
                                        Name: Mario Maugeri
                                        Title: Director of Operations


                                    /s/ Steven Heinemann
                                    ---------------------------------
                                    Steven Heinemann


                                    /s/ Doug Lipton
                                    ----------------------------------
                                    Doug Lipton


                                    /s/ Jay Goldstein
                                    ----------------------------------
                                    Jay Goldstein



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