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 January 2004

Commission File Number:  0-30628


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

                   21A Habarzel Street, Tel Aviv 69710, Israel
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                     (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 January 19, 2003             3







                                       2

                                                                       EXHIBIT 1

CONTACTS
Dafna Gruber, CFO                         Carmen Deville
+972 3 645 6252                           760-517-3188
760-517-3187
dafna.gruber@alvarion.com                 carmen.deville@alvarion.com
-------------------------                 ---------------------------


                                                           FOR IMMEDIATE RELEASE



          ALVARION RECOGNIZED AS BROADBAND WIRELESS MARKET SHARE LEADER
          -------------------------------------------------------------
                  WORLDWIDE WITH DEPLOYMENTS IN 130 COUNTRIES
                  -------------------------------------------

                                   - - - - - -

RECENT PYRAMID RESEARCH REPORT CHRONICLES COMPANY'S 45 PERCENT MARKET SHARE



TEL AVIV, ISRAEL AND CARLSBAD, CA JANUARY 19, 2004 - Alvarion Ltd. (NASDAQ:
ALVR), today announced that a recent report (November 2003) from Pyramid
Research has recognized the company's leading position in the global Broadband
Wireless Access market, measuring its market share at 45 percent. Participating
in WCA'S 10TH ANNUAL TECHNICAL SYMPOSIUM AND BUSINESS EXPO in San Jose, CA from
January 20 - 23 (booth #203), the company disclosed that its systems now provide
service to millions of users in 130 countries with over 1.5 million CPEs
deployed to date. Internal company calculations estimate that the total area
covered is over 1 million square miles or roughly the size of Western Europe.

With products covering all major bands from 900 MHz to 28 GHz, Alvarion
solutions are used by more than 3,000 global carriers, national ILECs, and other
service providers. In North America alone, Alvarion systems provide broadband
connections to users in over 5,000 cities and towns.

"In a market where many vendors claim leadership in one niche or another,
Alvarion is the overall leader in BWA as demonstrated by actual commercial
deployments of wireless broadband systems," remarked John Yunker, analyst at
Pyramid Research. "And Alvarion is well positioned to lead the rapidly evolving
WiMAX-Certified market in the years ahead."


                                       3

Since donating the core technology to form the first wireless broadband standard
ten years ago, Alvarion has had a significant leadership role in all major
technology innovations in the industry to date. Most recently, the company
leveraged its three years of OFDM deployments to help produce the 802.16a
specification and lead its harmonization with ETSI, and to be a principal
founder of the WiMAX Forum, a group chartered to ensure interoperable 802.16
systems. And in July 2003, the Company announced that it signed a strategic
agreement with Intel to work together to incorporate Intel's pioneering IEEE
802.16 compliant silicon into the Company's coming line of next generation
WiMAX-Certified, interoperable BWA systems.

"Our leadership position is a testament to the substantial technology
investments we have made and our singular focus on broadband wireless access
over the past decade," commented Zvi Slonimsky, CEO of Alvarion. "Our
comprehensive product portfolio allows our customers to have a winning business
case whatever connectivity challenge they face. We are now proactively building
on this foundation by leading the march to standards-based BWA solutions, and
our WiMAX Forum work and collaboration with Intel are both aimed at realizing
that vision."

The expected benefit of WiMAX-Certified systems to operators is the widespread
availability of high-performance wireless systems that will support varied
services such as high-speed data, voice and video, and feature vendor
interoperability and dramatic cost reductions relative to today's proprietary
systems.


                                       ###

ABOUT ALVARION
--------------
Alvarion is dedicated to delivering seamless wireless broadband networking
infrastructure to carriers, ISPs and private network operators, in order to
leverage their broadband opportunities into sustainable profits. Alvarion offers
premier wireless broadband solutions for access in the last mile, backhauling
connection to the backbone and private network connectivity. Featuring the
industry's most extensive range of products and international support, Alvarion
is a pioneering leader of the converged wireless broadband network. With over
1.5 million units deployed in 130 countries worldwide, Alvarion provides secure
rich-media networks for business or residential Internet access, corporate VPNs,
cellular base station feeding, community interconnection, public safety
connectivity and extended Hotspots.

Having recently acquired InnoWave's wideband access portfolio and expertise,
Alvarion provides a complete wireless solution that supports a wide range of
frequency bands, customer profiles and service types.

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

           This press release may contain 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 inability 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. WiMAX Forum and WiMAX-Certified are
trademarks of the WiMAX Forum.

YOU MAY REGISTER TO RECEIVE ALVARION'S FUTURE PRESS RELEASES OR AN INVESTOR KIT
INCLUDING BY CONTACTING CARMEN DEVILLE, INVESTOR RELATIONS:
CARMEN.DEVILLE@ALVARION.COM OR 760-517-3188.


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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: January 19, 2004                        By: /s/ Dafna Gruber
                                                 -------------------------------
                                              Name:  Dafna Gruber
                                              Title: Chief Financial Officer





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