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  June 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, June 2, 2004             3




                                       2



                                   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: June 2, 2004                        By: /s/ Tzvika Friedman
                                             ----------------------------
                                          Name:  Tzvika Friedman
                                          Title: President & COO




                                       4



                                                                       Exhibit 1


Investor Contacts:                  Press Contact:
--------------------------------------------------
Dafna Gruber, CFO                   Dan Guitteau
+972 3 645 6252                     972.998.7480
760-517-3187                        dguitteau@golinharris.com
dafna.gruber@alvarion.com
-------------------------

Carmen Deville
760-517-3188                                             FOR IMMEDIATE RELEASE
carmen.deville@alvarion.com
---------------------------


  ALVARION LAUNCHES BREEZEMAX, ITS WIMAX PLATFORM DEVELOPED FROM THE GROUND UP
                     BASED ON IEEE 802.16/HIPERMAN STANDARDS
                                     -------
                       New System Passed Successful Pilots
                        With Operators in Europe and Asia

Washington, D.C. and Tel Aviv, Israel, June 2, 2004 - Alvarion Ltd. (NASDAQ:
ALVR), the global leader in wireless broadband solutions, today launched its
WiMAX(TM) platform, BreezeMAX, augmenting its leading product portfolio. Based
on the IEEE 802.16/ETSI HiperMAN standards and WiMAX Forum profiles, BreezeMAX
incorporates core wireless innovations and leverages Alvarion's ten-plus years
of experience deploying OFDM systems in commercial broadband wireless access
(BWA) networks. With prominent roles in the WiMAX ForumTM and a history of
driving global wireless standards, Alvarion's significant investment in research
and development has resulted in a carrier-class platform that delivers a host of
high bandwidth applications from residential to business, MDU/MTU, hotspot
backhauling and home networking. The BreezeMAX platform is designed to support
WiMAX certified CPEs, which will incorporate the Intel WiMAX chip set as they
become available in the market.

The initial release of the WiMAX platform, BreezeMAX 3500, operates in the
3.5GHz frequency band, and has already successfully passed rigorous testing with
operators in Europe and Asia Pacific, some of which plan to deploy the system
commercially starting in Q3 2004.

"The launch of products that provide a path for operators to WiMAX
standardisation is an important development for the industry," said Michael
Philpott, Senior Analyst with Ovum and broadband expert.
 "Equipment standardisation is essential if the fixed wireless market is to grow
and service providers will demand it. WiMAX brings this standardisation and
should assure a place for fixed wireless in the future broadband access market."

BreezeMAX represents Alvarion's third-generation OFDM platform with advanced
Non-Line-of-Sight (NLOS) functionality. The platform is designed to take BWA to
widespread deployment by both small and large carriers because of its cost
improvement over current solutions, thus creating a faster return on investment.
Its carrier-class design supports quality of service (QoS) and broadband speeds
to enable carriers to offer both data and toll-quality voice to thousands of
subscribers in a single cell.

"BreezeMAX is the culmination of Alvarion's decade of BWA technological
leadership, our founding role in the WiMAX Forum, and our WiMAX development
partnership with Intel," said Rudy Leser, VP Marketing of Alvarion. "Our WiMAX
platform has been built from scratch; we did not take the easy



route and adapt existing products to meet the expected WiMAX standard. Instead
we invested time, resources and energy into developing an entirely new product
based on what the market now, and in the future, will require."

BreezeMAX is a modular, scalable platform that offers macro and micro base
stations, for dense urban to rural areas. The platform also has a rich portfolio
of customer premise equipment (CPE) to address business and residential user
markets. The variety of CPEs provide very cost effective solutions that support
multiple applications such as IP-based voice and data, including multi-port
devices for MDU/MTU, indoor Wi-Fi connectivity, firewall and advanced IP
functions for home networking and Hotspot backhauling. These offerings make
BreezeMAX the optimal BWA solution for operators intending to significantly
boost their revenue potential.

BreezeMAX has a flexible architecture to support future enhancements such as
smart antennas, OFDMA, zero install and mobility. It will continue to follow
closely the evolution of IEEE 802.16 standards as reflected in the roadmap of
the Intel WiMAX chips and will support additional frequency bands, duplexing
schemes, and services as a WiMAX evolution of Alvarion product lines.


* Other brand and trademarks are property of their respective owners.

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. With the industry's most extensive portfolio covering the
full range of frequency bands, Alvarion's products enable the delivery of
business and residential broadband access, corporate VPNs, toll quality
telephony, mobile base station feeding, Hotspot coverage extension, community
interconnection, and public safety communications. Alvarion works with several
leading OEM providers and over 200 local partners to support its diverse
customer base in solving their last mile connection challenges.

As an industry pioneer, Alvarion has been driving and delivering wireless
broadband innovations for 10 years from core technology developments to creating
and promoting industry standards. Leveraging its leading roles in the IEEE and
HiperMAN standards committees and experience deploying OFDM-based systems, the
company's prominent work in the WiMAX ForumTM 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.