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                                    Form 6-K

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                        Report of Foreign Private Issuer

                        Pursuant to Rule 13a-16 or 15d-16
                     of the Securities Exchange Act of 1934

                          For the month of August, 2004

                              CONVERIUM HOLDING AG
                   ------------------------------------------
                 (Translation of registrant's name into English)

                                 Baarerstrasse 8
                                   CH-6300 Zug
                                   Switzerland
             -------------------------------------------------------
                    (Address of principal executive offices)

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

                       Form 20-F    X    Form 40-F
                                 -------           -------

Indicate by check mark whether the registrant by furnishing the information
contained in this Form 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 the file number assigned to the registrant in
connection with Rule 12g3-2(b): 82- Not Applicable






Fidelity adjusts its holding in Converium shares from 9.87% to 3.51%



Converium Holding Ltd hereby informs that Fidelity International Limited,
Pembroke Hall, 42 Crow Lane, Hamilton, Bermuda, has reduced its holding from
3,937,468 registered shares in Converium Holding Ltd, Zug to 1,402,599 with
voting rights. This corresponds to a reduction from 9.87% to 3.51% of
Converium's registered shares with voting rights.


Zug, August 3, 2004

For further information:

Esther Gerster                                     Zuzana Drozd
Manager Corporate Communications                   Head of Investor Relations
esther.gerster@converium.com                       zuzana.drozd@converium.com
+41 (0)1 639 90 22                                 +41 (0)1 639 91 20

www.converium.com






                                   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.


                                 CONVERIUM HOLDING AG




                                 By:  /s/ Dirk Lohmann
                                      Name:      Dirk Lohmann
                                      Title:     CEO




                                 By:  /s/ Christian Felderer
                                      Name:      Christian Felderer
                                      Title:     General Legal Counsel



Date:  August 3, 2004