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                                    Form 6-K

                             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 May, 2007

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

                                 Dammstrasse 19
                                   CH-6301 Zug
                    (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

News release
Converium Holding Ltd, Zug

Zug, Switzerland - May 10, 2007 - Converium advises shareholders to accept
improved offer of CHF 23.2 by French reinsurer SCOR

Converium's Board of Directors unanimously welcomes today's revised offer from
SCOR S.A. The Board therefore recommends that shareholders accept the improved
offer. This decision is fully supported by all members of the Global Executive

Under the terms of SCOR's revised offer, each Converium share may be exchanged
for 0.5 new SCOR shares plus CHF 5.5 in cash and further foresees that the
consideration will not be reduced by Converium's proposed gross dividend of CHF
0.2 per Converium share. Previously the offer was 0.5 new SCOR shares plus CHF 4
in cash. Based on the closing price of SCOR shares on Euronext Paris on May 9,
2007, the Offer Price values each Converium share at CHF 23.2.

Converium shareholders will also benefit from SCOR's proposed dividend for the
business year 2006 of
EUR 0.8 per SCOR share, as they will receive for each tendered Converium Share
an equivalent amount of CHF 0.66 in cash which equals 50% of the amount of the
dividend paid (in EUR) per SCOR share.

"The increase in the offer price represents a significant improvement in the
consideration offered to our shareholders," said Markus Dennler, Chairman of
Converium's Board of Directors. "The offer price recognizes our remarkable
turnaround of the past two years. It further reflects the exceptional quality of
our staff, longstanding client relationships and excellent growth prospects
supported by a strong capital position."

Converium's Global Executive Committee is committed to ensuring a smooth
combination of the two businesses. This includes the desire to maximize the
value of synergies and to facilitate the retention of talent and clients.

For purposes of these calculations, the following currency exchange rate has
been applied (closing price of May 9, 2007): EUR 1 = CHF 1.648.


Beat W. Werder                                  Marco Circelli

Head of Public Relations                        Head of Investor Relations             

Phone:     +41 44 639 90 22                     Phone:      +41 44 639 91 31

Fax:       +41 44 639 70 22                     Fax:        +41 44 639 71 31

Dr. Kai-Uwe Schanz                              Inken Ehrich
Chief Communication &
Corporate Development Officer                   Investor Relations Specialist          

Phone:     +41 44 639 90 35                     Phone:      +41 44 639 90 94

Fax:       +41 44 639 70 35                     Fax:        +41 44 639 70 94

About Converium

Converium is an independent international multi-line reinsurer known for its
innovation, professionalism and service. Today Converium employs about 500
people in 15 offices around the globe and is organized into three business
segments: Standard Property & Casualty Reinsurance, Specialty Lines and Life &
Health Reinsurance. Converium has an "A-" ("strong") financial strength rating
(outlook stable) from Standard & Poor's and a "B++" financial strength rating
(outlook positive) from A.M. Best Company.

Important Disclaimers

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 `seek to', `expects', `aims' `should continue',
`believes', `anticipates', `estimates' and `intends'. The specific
forward-looking statements cover, among other matters, the Company's strategy
and management objectives, our growth prospects and our ability to ensure a
smooth transition of our business with that of SCOR. 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 whether we are able to secure an upgrade
of our financial strength ratings; our ability to refinance our outstanding
indebtedness and increase our use of hybrid capital; uncertainties of
assumptions used in our reserving process; risk associated with implementing our
business strategies and our capital improvement measures; cyclicality of the
reinsurance industry; the occurrence of natural and man-made catastrophic events
with a frequency or severity exceeding our estimates; acts of terrorism and acts
of war; changes in economic conditions, including interest and currency rate
conditions that could affect our investment portfolio; actions of competitors,
including industry consolidation and development of competing financial
products; a decrease in the level of demand for our reinsurance or increased
competition in our industries or markets; our ability to expand into emerging
markets; our ability to enter into strategic investment partnerships; a loss of
our key employees or executive officers without suitable replacements being
recruited within a suitable period of time; our ability to address material
weaknesses we have identified in our internal control environment; political
risks in the countries in which we operate or in which we reinsure risks; the
passage of additional legislation or the promulgation of new regulation in a
jurisdiction in which we or our clients operate or where our subsidiaries are
organized; the effect on us and the insurance industry as a result of the
investigations being carried out by the US Securities and Exchange Commission,
New York's Attorney General and other governmental authorities; our ability to
regain past customers following any rating upgrades and the resolution of the
investigations being carried out by the US Securities and Exchange Commission,
New York's Attorney General and other governmental authorities; changes in our
investment results due to the changed composition of our invested assets or
changes in our investment policy; failure of our retrocessional reinsurers to
honor their obligations or changes in the credit worthiness of our reinsurers;
our failure to prevail in any current or future arbitration or litigation; and
extraordinary events affecting our clients, such as bankruptcies and
liquidations, and other risks and uncertainties, including those detailed in the
Company's filings with the U.S. Securities and Exchange Commission (including,
but not limited to, our Annual Report on Form 20-F filed 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.


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: May 16, 2007