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 May 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 May 5, 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: May 5, 2004.                  By: /s/ Dafna Gruber
                                      -----------------------------
                                    Name:  Dafna Gruber
                                    Title: Chief Financial Officer





                                       3