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 November, 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





                                   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:  November 4, 2004





                           Converium Holding Ltd, Zug


Zug, Switzerland - November 4, 2004 - Martin Kauer leaves Converium

Converium announces that Martin A. Kauer, Group CFO of Converium, intends to
leave the Company effective early 2005.

The Board of Directors has taken note of Mr. Kauer's intended departure and
thanks him for his efforts for Converium and for his ensuring continuity of
management during the period of transition. This will allow the Board to find a
suitable successor.

A search and recruitment process is under way. Mr. Kauer's successor will be
appointed in due time.

                                  * * * * * * *

Enquiries:
Michael Schiendorfer                       Zuzana Drozd
Media Relations Manager                    Head of Investor Relations

michael.schiendorfer@converium.com         zuzana.drozd@converium.com

Phone:         +41 (0) 1 639 96 57         Phone:         +41 (0) 1 639 91 20
Fax:           +41 (0) 1 639 76 57         Fax:           +41 (0) 1 639 71 20

About Converium

Converium is an independent international multi-line reinsurer known for its
innovation, professionalism and service. Today Converium employs more than 800
people in 20 offices around the globe and is organized into three business
segments: Standard Property & Casualty Reinsurance, Specialty Lines and Life &
Health Reinsurance. Converium has a "BBB+" rating (outlook stable) from Standard
& Poor's and a "B++" rating (outlook stable) from A.M. Best Company.

Important Disclaimer

This document contains forward-looking statements as defined in the U.S. Private
Securities Litigation Reform Act of 1995. It contains forward-looking statements
and information relating to the Company's financial condition, results of
operations, business, strategy and plans, based on currently available
information. These statements are often, but not always, made through the use of
words or phrases such as 'expects', 'should continue', 'believes',
'anticipates', 'estimates' and 'intends'. The specific forward-looking
statements cover, among other matters, the reinsurance market, the outcome of
insurance regulatory reviews, the Company's operating results, the rating
environment and the prospect for improving results, the amount of capital
required and impact of its capital improvement measures, including the
restructuring of our U.S. business and its reserve position. Such statements are
inherently subject to certain risks and uncertainties. Actual future results and
trends could differ materially from those set forth in such statements due to
various factors. Such factors include general economic conditions, including in
particular economic conditions; the frequency, severity and development of
insured loss events arising out of catastrophes, as well as man-made disasters;
the outcome of our regular quarterly reserve review, our ability to raise
capital and the success of our capital improvement measures, the ability to
obtain applicable regulatory approval for our capital improvement measures, the
ability to exclude and to reinsure the risk of loss from terrorism; fluctuations
in interest rates; returns on and fluctuations in the value of fixed-income
investments, equity investments and properties; fluctuations in foreign currency
exchange rates; rating agency actions; changes in laws and regulations and
general competitive factors, and other risks and uncertainties, including those
detailed in the Company's filings with the U.S. Securities and Exchange
Commission and the SWX Swiss Exchange. The Company does not assume any
obligation to update any forward-looking statements, whether as a result of new
information, future events or otherwise.

www.converium.com