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 November 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 is included in this report on Form 6-K:

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

       1.         Press release, dated November 3, 2004          4






                                       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: November 3, 2004              By: /s/ Dafna Gruber
                                       -----------------------------
                                    Name:  Dafna Gruber
                                    Title: Chief Financial Officer









                                       3



                                                                       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 AGAIN ACHIEVES RECORD RESULTS
                          FOR THE THIRD QUARTER OF 2004

              Revenues Up 7%, Net Income Increased 47% Sequentially

TEL AVIV, Israel--Nov. 3, 2004--Alvarion Ltd. (NASDAQ: ALVR), the leading
provider of wireless broadband solutions worldwide, today announced financial
results for the third quarter ended September 30, 2004.


Revenues for the third quarter of 2004 rose to a record $52.2 million, an
increase of 7% compared to $48.8 million in the second quarter of 2004, and up
52% from $34.3 million in the third quarter of 2003. Gross margin increased for
the 12th consecutive quarter, reaching 44.3% compared to 43.2% in the second
quarter of 2004 and 41.1% in the third quarter of 2003.


According to US GAAP, net income increased to $3.7 million or $0.06 per share on
a fully diluted basis for the third quarter of 2004. GAAP net income for the
second quarter of 2004 was $2.5 million, or $0.04 per share on a fully diluted
basis, and GAAP net loss for the third quarter of 2003 was $(2.1) million, or
$(0.04) per share.


Revenues for the first 3 quarters of 2004 totaled to $145.6 million, an increase
of 66% compared with revenues of $87.7 million in the same period in 2003.
During the first 3 quarters of 2004, net income totaled to $7.6 million compared
to a net loss of $(11.9) million in the same period of 2003.


Results for all periods include expenses attributable to the amortization of
intangible assets and amortization of deferred stock compensation, which totaled
$680,000 in the second and third


                                       4



quarters of 2004, and $790,000 in the third quarter of 2003. Excluding all
aforementioned amortizations, the Company's non-GAAP net income for the third
quarter of 2004 was $4.4 million, or $0.07 per diluted share. For the second
quarter of 2004 non-GAAP net income was $3.2 million, or $0.05 per diluted
share, and for the third quarter of 2003 non-GAAP net loss was $(1.3) million,
or $(0.02) per share.


The Company generated $6.3 million in cash provided by operating activities in
the third quarter and the balance sheet remained very strong with its cash
position reaching a record $170 million at September 30, 2004. DSO was a record
low of 35 days.


Comments of Management

"Both technological and market leadership combined with strong execution led to
another outstanding quarter for the company," said Zvi Slonimsky, CEO of
Alvarion. "Once again we achieved improvement in all financial measurements.


"We are continuing to enhance our position as the leader in both broadband
wireless access and the adoption of the WiMAX standard. Our broad-based growth
in Q3 again reflected the increase in worldwide demand for wireless broadband
solutions. We also continue to see a high degree of interest in the WiMAX
standard. We were extremely gratified by the outstanding customer response to
the BreezeMAX 3500, our new WiMAX-ready system. Exemplifying the strong response
were two new BreezeMAX customers announced recently - Altitude Telecom, an
independent operator in France planning a nationwide WiMAX network, and
MobileCity, which is deploying the first WiMAX-ready network in Scandinavia.
During Q3, we received the first sample chips from Intel for the standard CPE.
We are pleased with the progress that Intel is making and we are on track for
having an Intel-based CPE in the market by mid-year 2005.


"During the third quarter, we continued to see strong demand for all product
groups from operators around the world. We were pleased by the follow-on orders
from existing Tier 1 incumbent carriers in Latin America, Europe, South Africa,
and China," continued Mr. Slonimsky. "We expect these regions to continue to be
sources of strong growth going forward. On October 16, 2004, we amended the
amalgamation agreement with interWAVE Communications International Ltd., a
leading supplier of compact cellular network infrastructure based on GSM and
CDMA2000 technology that is particularly well-suited for rural areas in
developing regions. We are currently awaiting approval of the deal by interWAVE
shareholders


                                       5



and, once completed, this acquisition will complement our existing wireless
solutions with a cost effective fixed and mobile solution to serve the need for
voice and data in regions of the world that need telecommunication
infrastructure. We intend to apply our experience in integrating acquisitions to
realize the benefits of the combined company," concluded Mr. Slonimsky.


Q4 2004 Guidance

The Company expects Q4 2004 revenues to range between $54 million and $56
million. At this revenue range, net earnings per share are expected to range
between 7 and 8 cents while non-GAAP net earnings per share, which excludes
amortization of intangible assets and deferred stock-based compensation, is
expected to range between 8 and 9 cents. The fourth quarter guidance also
excludes any impact on results of operations and any one time
transaction-related charges associated with the acquisition of interWAVE
Communications International Ltd., which the company hopes to close by the end
of Q4.


Alvarion's management will host a conference call today, November 3, 2004, at
9:00 a.m. Eastern Time to discuss the quarter's results. To participate in the
call, please dial one of the following numbers approximately five minutes prior
to the scheduled start time: USA: (480) 629-9034; International:
+1-480-629-9034.


The public is invited to listen to the live webcast of the conference call. For
details please visit Alvarion's website at www.alvarion.com. An archive of the
on-line broadcast will be available on the website. A replay of the call will be
available from 2:15 p.m. EDT on November 3, 2004 through 11:59 p.m. EDT on
November 10, 2004. To access the replay, please call USA: (320) 365-3844,
International: +1-320-365-3844. To access the replay, users will need to enter
the following code: 750667.


About Alvarion
With more than 2 million units deployed in 130 countries, Alvarion is the
worldwide leader in wireless broadband providing systems to carriers, ISPs and
private network operators. Leading the WiMAX revolution, Alvarion has the most
extensive deployments and proven product portfolio in the industry 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,

                                       6



and public safety communications. Alvarion works with several top OEM providers
and over 200 local partners to support its diverse global customer base in
solving their last-mile challenges.
 
As a wireless broadband pioneer, Alvarion has been driving and delivering
innovations for over 10 years from core technology developments to creating and
promoting industry standards. Leveraging its key 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 increasing widespread adoption
of standards-based products in the wireless broadband market.

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.




                                       7