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 July, 2005

                              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





Zurich Cantonal Bank increases its holding of Converium's registered shares to
5.001% and reduces again to below 5% Disclosure of shareholdings pursuant to
Art. 20 SESTA

Zug, Switzerland - July 7, 2005 - Converium Holding Ltd has been notified that
Zurich Cantonal Bank, Tessinerplatz 7, 8002 Zurich, Switzerland, adjusted its
holding of registered shares of Converium Holding Ltd, Zug on June 29, 2005 to
5.001% and on June 30, 2005 to below 5%.


Zurich Cantonal Bank states that the above-mentioned stock of shares is a pure
trading position, which is generated during the normal course of its derivative
business.


Contacts:

Zuzana Drozd
Head of Investor Relations
zuzana.drozd@converium.com
--------------------------
Phone    +41 (0) 44 639 91 20
Fax      +41 (0) 44 639 71 20


Esther Gerster
Head of Public Relations
esther.gerster@converium.com
----------------------------
Phone    +41 (0) 44 639 90 22
Fax      +41 (0) 44 639 70 22



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/ Terry Clarke
                                           ----------------
                                           Name:      Terry Clarke
                                           Title:     CEO


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



Date: July 8, 2005