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 September, 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
                                    --------------



                           Converium Holding Ltd, Zug

Zug,   Switzerland  -  September  10,  2004  -  Converium  today  announces  the
appointment of Terry G. Clarke to the position of Managing Director of Converium
Holding Ltd.

The Board of Directors of Converium Holding Ltd today announces the appointment,
with immediate  effect,  of its member Terry G. Clarke,  F.I.A.,  age 62, to the
position of Managing  Director.  Mr Clarke,  a British  citizen,  will  actively
support the Chief Executive  Officer,  Dirk Lohmann,  and his management team in
running the Company.  He will be responsible for enhancing the  effectiveness of
strategic  and  operational  decision-making.  Mr Clarke  will  continue to be a
member of the Board of Directors.

Peter C.  Colombo,  Chairman  of the Board of  Directors,  stated:  "Converium's
current short-term  challenges require a closer collaboration  between the Board
of Directors and the Global Executive Committee. Going forward, Mr Clarke's role
will be to provide an interface  between the Board and the management team. I am
convinced  that this move will help Converium to  successfully  meet the current
and future challenges facing the Company."

Terry G. Clarke was a consulting  actuary with Tillinghast,  Towers Perrin and a
Principal  of  Towers  Perrin.  He  joined  their  London  office  in 1986  and,
immediately  prior to his retirement at the end of 2001, was Managing  Principal
of Tillinghast's  North America  practice.  Previously,  from 1978 until 1986 Mr
Clarke was a member of the Norwich  Winterthur  Group  senior  management  team.
Prior to 1978, he held various  positions in the Norwich Union Group.  Mr Clarke
is a Fellow of the Institute of Actuaries and has been  co-author of a number of
papers on non-life insurance  subjects as well as a tutor and examiner.  He is a
member of a number of professional committees both in the U.K. and in Europe.

                                  * * * * * * *

Enquiries:

Dr Kai-Uwe Schanz                               Zuzana Drozd
Chief Communication Officer                     Head of Investor Relations

kai-uwe.schanz@converium.com                    zuzana.drozd@converium.com

Phone:        +41 (0) 1 639 90 35               Phone:      +41 (0) 1 639 91 20
Fax:          +41 (0) 1 639 70 35               Fax:        +41 (0) 1 639 71 20

About Converium

Converium is an independent  leading global  multi-line  reinsurer known for its
innovation, professionalism and service. Today Converium ranks among the top ten
professional  reinsurers  and  employs  approximately  850  people in 23 offices
around the globe. Converium is organized into three business segments:  Standard
Property & Casualty Reinsurance,  Specialty Lines and Life & Health Reinsurance.
Converium's  net losses for the  September  11,  2001  terrorist  attacks in the
United  States are capped at US$ 289.2  million  by its  former  parent,  Zurich
Financial Services. Converium has minimal A&E exposures.  Converium has an "A -"
rating (watch  negative) from Standard & Poor's and a "B++"  (outlook  negative)
rating 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.

Please note that the  company has made it a policy not to provide any  quarterly
or annual  earnings  guidance  and it will not update any past  outlook for full
year earnings.  It will however provide  investors with perspective on its value
drivers,  its strategic  initiatives and those factors critical to understanding
its business and operating environment.

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:  September 17, 2004