UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    Form 6-K

                        REPORT OF FOREIGN PRIVATE ISSUER

                        PURSUANT TO RULE 13a-16 OR 15d-16
                     OF THE SECURITIES EXCHANGE ACT OF 1934

For the month of July 2004

Commission File Number:  0-30628


                                  ALVARION LTD.
 ------------------------------------------------------------------------------
                 (Translation of registrant's name into English)

                   21A Habarzel Street, Tel Aviv 69710, Israel
 ------------------------------------------------------------------------------
                     (Address of principal executive office)

Indicate by check mark whether the registrant files or will file annual reports
under cover of Form 20-F or Form 40-F.
Form 20-F |X|   Form 40-F |_|

Indicate by check mark if the registrant is submitting the Form 6-K in paper
as permitted by Regulation S-T Rule 101(b)(1): ____

Indicate by check mark if the registrant is submitting the Form 6-K in paper
as permitted by Regulation S-T Rule 101(b)(7): ____


Indicate by check mark whether by furnishing the information contained in this
Form, the registrant is also thereby furnishing the information to the
Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.
Yes |_| No |X|

If "Yes" is marked, indicate below the file number assigned to the registrant
in connection with Rule 12g3-2(b): 82-___________




The following are included in this report on Form 6-K:

                                                           Sequential
     Exhibit               Description                     Page Number
     -------               -----------                     -----------

       1.         Press release, dated July 6, 2004              3




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                                   SIGNATURES


            Pursuant to the requirements of the Securities Exchange Act of 1934,
the registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.


                                          ALVARION LTD.



Date: July 6, 2004                        By: /s/ Dafna Gruber
                                             ----------------------------
                                          Name:  Dafna Gruber
                                          Title: Chief Financial Officer




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                                    EXHIBIT 1

MILLICOM ARGENTINA, ALVARION AND INTEL JOIN FORCES TO LAUNCH THE FIRST WIMAX(TM)
NETWORK IN LATIN AMERICA

The network will provide broadband access to urban and rural zones as well as
underdeveloped areas that currently lack cable or ADSL services.

Buenos Aires, Argentina and Tel-Aviv, Israel, July 6, 2004 - Millicom Argentina,
the main provider of wireless network solutions such as broadband, Virtual
Private Networks (VPNs), Voice over IP (VoIP) and Wi-Fi, proudly announces
together with Alvarion (NASDAQ: ALVR) and Intel, the launch of the first
WiMAX(TM) network in Latin America, to be held during the months of September to
December 2004.

In the world of broadband wireless access technologies, WiMAX is the result of a
natural evolution and standardization of the Alvarion technology that Millicom
has been using in Argentina since the year 2000. The main benefits of the WiMAX
technology are greater broadband, quality of service and down the road, mobility
within the metropolitan area or within a radius of 30 km., with no loss of
connection whatsoever at speeds of over 2MB/sec.

WiMAX antennas are capable of transmitting high-speed connections for Internet
to businesses and homes located at long distances. Thus, eliminating cable
connections in buildings and offices to access voice services or the Internet.

"The WiMAX technology will enable real wireless mobility. In other words, it
will give us the freedom to use our laptops or PDAs to access the Internet or
transmit voice with greater capacity and better quality of service than other
current options", expressed Luis Galli, General Manager of Millicom Argentina.
"It is fundamental to be at the forefront in the development of wireless access
solutions. To work together with Intel and Alvarion, main providers of wireless
solutions and WiMAX worldwide, guarantees our success and strengthens our
position in the market and the compromise assumed with our customers in 2003, by
creating a more ample and innovative national broadband wireless network in
Argentina with presence in over 40 cities".

Esteban Galuzzi, General Manager of Intel for the South America region
highlighted: "Intel's vision is one in which laptops and PDAs, or any other
digital device, can communicate with one another, wherever they might be. WiMAX
is the natural evolution of Wi-Fi because with this new technology of broader
reach, we could access the Internet from any place with the same simplicity and
convenience benefits the cell phones have today".

Alvarion's BreezeMAX (TM) WiMAX Platform will be launched in urban, suburban and
rural areas in Argentina. BreezeMAX is a high-performance broadband wireless
solution built from the ground up to comply with IEEE 802.16/ETSI HiperMAN
standards and WiMAX Forum profiles.

"In the culmination of Alvarion's decade of BWA technological leadership, its
founding role in the WiMAX Forum, and its WiMAX development partnership with
Intel, BreezeMAX incorporates core wireless innovations and leverages Alvarion's
several years of experience deploying OFDM systems in commercial broadband
wireless access (BWA) networks," commented Zvi Slonimsky, CEO of Alvarion.


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BreezeMAX is a carrier-class platform that can support thousands of users while
supporting numerous broadband applications from residential to business,
MDU/MTU, hotspot backhauling and home networking.

                            About Millicom Argentina

Millicom Argentina initiated activities in the year 2000 with the help of
Sociedad Comercial del Plata, incorporating in the market network wireless
solutions: Broadband Internet, Virtual Private Networks (VPN), Voice over IP
(VoIP) and Wi-Fi. Today, they have successfully installed equipment in several
main corporations with over 6400 active customers. Their customers keep adding
up, looking for innovative products which they can trust. Their main customers
are Petrobras, Repsol-YPF, Cisco Systems, Productos Roche, Supermercados Coto,
Barujel Azulay, Western Union, Aerolineas Argentinas, Pulte, Bed Time, TGN
(Transportadora Gas del Norte), Musimundo, Pecom Energia, TGS (Transportadora
Gas del Sur), Village Cinema, La Caja de Ahorros y Seguros, Banco Credicoop,
Sion, Impsat, Prima, Netizen, Techtel, Leader Price, Maxiconsumo, Red Megatone,
Havanna, Pago Facil, Cencosud among others.

To get more information about Millicom and their solutions, please visit
www.millicom.com.ar or call 0810-810-1000 / 011-40028100.

For more information:

Agustina Mitjavila
IMS Marketing
011-4807-6380
amitjavila@imsmarketing.com

About  Intel:
-----  ------

Intel, the largest manufacturer of computer chips in the world, is also the
leader in the manufacture of computers, networks and communications. For more
information, visit www.intel.com.

For more information:

Karina stocovaz
kstocovaz@muchnikpr.com
-----------------------
Fernanda Cometto
fcometto@muchnikpr.com
----------------------

Muchnik, Alurralde, Jasper & Asoc/ socio de MS&L
Tel. 5031-1300 (lineas rotativas)


About Alvarion:
---------------

With over 2 million units deployed in 130 countries, Alvarion is the worldwide
leader in wireless broadband providing systems to carriers, ISPs and private
network operators. Featuring the industry's most extensive portfolio and
covering the full range of frequency bands, the company's products enable the
delivery of business and residential broadband access, corporate VPNs,


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mobile base station feeding, Hotspot coverage extension, community
interconnection, and public safety communications. Alvarion works with several
leading OEM providers and through over 200 local partners to support its diverse
customer base in solving their last mile connection challenges wherever located.

As an industry pioneer, Alvarion has been driving and delivering wireless
broadband innovations for over 10 years from core technology developments to
creating and promoting industry standards. Most recently offering OFDM-based
systems and taking leading roles in the IEEE, HiperMAN standards and the
company's prominent work in the WiMAX Forum(TM) which is focused on leading the
wireless broadband market to widespread adoption of standards-based products.

 For more information, visit Alvarion's World Wide Web site at www.alvarion.com
                                                               ----------------

This press release contains forward -looking statements within the meaning of
the "safe harbor" provisions of the Private Securities Litigation Reform Act of
1995. These statements are based on the current expectations or beliefs of
Alvarion's management and are subject to a number of factors and uncertainties
that could cause actual results to differ materially from those described in the
forward -looking statements. The following factors, among others, could cause
actual results to differ materially from those described in the forward-looking
statements: inability to further identify, develop and achieve success for new
products, services and technologies; increased competition and its effect on
pricing, spending, third-party relationships and revenues; as well as the in
ability to establish and maintain relationships with commerce, advertising,
marketing, and technology providers and other risks detailed from time to time
in filings with the Securities and Exchange Commission.

Information set forth in this press release pertaining to third parties has not
been independently verified by Alvarion and is based solely on publicly
available information or on information provided to Alvarion by such third
parties for inclusion in this press release. The web sites appearing in this
press release are not and will not be included or incorporated by reference in
any filing made by Alvarion with the Securities and Exchange Commission, which
this press release will be a part of.

You may request Alvarion's future press releases or a complete Investor Kit by
contacting Carmen Deville, Investor Relations: carmen.deville@alvarion.com or
+1-760-517-3188.

Investor Contacts:
------------------
Dafna Gruber, CFO
+972 3 645 6252
760-517-3187
dafna.gruber@alvarion.com
-------------------------

Carmen Deville
760-517-3188
carmen.deville@alvarion.com
---------------------------
Press Contact:
--------------
Dan Guitteau
972.998.7480
dguitteau@golinharris.com



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