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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 June, 2006

                              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 10.45% Disclosure of shareholdings pursuant to Art. 20 SESTA

Zug, Switzerland - June 21, 2006 - Converium Holding Ltd has been notified that
Zurich Cantonal Bank, Tessinerplatz 7, 8002 Zurich, Switzerland, increased its
holding of registered shares of Converium Holding Ltd, Zug to 10.45% or
15,334,360 registered shares with voting rights.



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/ Inga Beale
                                         Name:      Inga Beale
                                         Title:     CEO




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



Date: June 23, 2006