Exhibit 3.1


                                                  Final Schedule to the Bye-laws
                                                      of Arch Capital Group Ltd.


                           CERTIFICATE OF DESIGNATIONS

                                       OF

                     SERIES A CONVERTIBLE PREFERENCE SHARES


     The terms of the authorized Preference Shares (as defined below) of Arch
Capital Group Ltd., a company incorporated under the laws of Bermuda (the
"Company"), shall be as set forth below in this Schedule to the Bye-laws of the
Company (this "Schedule").

     (a) Designation. (1) There is hereby created from the authorized and
unissued preference shares of the Company a series of convertible preference
shares designated as the Company's "Series A Convertible Preference Shares" (the
"Preference Shares") as designated by the Board of Directors. Each Preference
Share will have a liquidation preference of $21.00 (the "Liquidation
Preference").

     (2) All Preference Shares purchased, exchanged, converted or otherwise
acquired by the Company shall be repurchased and canceled and, upon the taking
of any action required by applicable law, shall be restored to the status of
authorized but unissued preference shares of the Company, without designation as
to series, and may thereafter be reissued.

     (b) Currency. All Preference Shares shall be denominated in United States
currency, and all payments and distributions thereon or with respect thereto
shall be made in United States currency. All references herein to "$" or
"dollars" refer to United States currency.

     (c) Ranking. The Preference Shares shall, with respect to dividend rights
and rights upon liquidation, winding up or dissolution, rank (1) prior to each
other class or series of shares of the Company except Parity Shares and (2) on a
parity with Parity Shares. For purposes hereof, (A) "Junior Shares" shall mean
the Common Shares of the Company, par value $0.01 per share (the "Common
Shares") and the shares of any other class or series of equity securities of the
Company which,



                                       -2-


by the terms of the Bye-laws of the Company or of the instrument by which the
Board of Directors shall fix the rights, preferences and limitations thereof,
shall not be designated as ranking on a parity with the Preference Shares in
respect of dividend rights and rights upon liquidation, winding up or
dissolution and (B) "Parity Shares" shall mean the shares of any other class or
series of equity securities of the Company which, by the terms of the Bye-laws
of the Company or of the instrument by which the Board of Directors shall fix
the rights, preferences and limitations thereof, shall, in the event that the
dividends thereon are not paid in full, be entitled to share ratably with the
Preference Shares, or shall, in the event that the amounts payable thereon on
liquidation are not paid in full, be entitled to share ratably with the
Preference Shares in any distribution of assets other than by way of dividends
in accordance with the sums which would be payable in such distribution if all
sums payable were discharged in full.

     (d) Dividends. The holders of Preference Shares shall be entitled to
receive, from funds legally available therefor, dividends payable when, as and
if dividends (including, without limitation, any dividend consisting of stock or
other securities or property or rights or warrants to subscribe for securities
of the Company or any of its subsidiaries by way of dividend or spin-off) are
declared by the Board of Directors with respect to the Common Shares. Dividends
shall be payable on each outstanding Preference Share in an amount per
Preference Share equal to the amount of such dividends as would be payable with
respect to the number of Common Share(s) into which such Preference Share is
convertible pursuant to paragraphs (g)(1) and (h). No dividends may be paid or
declared on or with respect to the Common Shares prior to the declaration and
payment of a dividend on or with respect to the Preference Shares. Dividends
shall be non-cumulative.

     (e) Liquidation Preference. (1) Upon any voluntary or involuntary
liquidation, dissolution or winding up of the Company or a reduction or decrease
in the Company's shares resulting in a distribution of assets to the holders of
any class or series of the Company's shares, each holder of Preference Shares
shall be entitled to payment out of the assets of the Company available for
distribution of an amount equal to the then effective Liquidation Preference per
Preference Share held by such holder, plus all accumulated and unpaid dividends
thereon, before any distribution is made on any Junior Shares, including,
without limitation, Common Shares. If, upon any voluntary or involuntary
liquidation, dissolution or winding up of the Company or a reduction or decrease
in the Company's capital Shares, the amounts payable with respect to Preference
Shares and all other Parity Shares are not paid in full, the holders of
Preference Shares and the holders of the Parity Shares shall share equally and
ratably in any distribution of assets of the Company in proportion to the full
liquidation preference and all accumulated and unpaid dividends to which each
such holder is entitled.

     (2) Neither the voluntary sale, conveyance, exchange or transfer (for cash,
shares, securities or other consideration) of all or substantially all of the
property or assets of the Company nor the consolidation, merger or amalgamation
of the Company with or into any person or the consolidation, merger or
amalgamation of any person with or into the Company shall alone be deemed to be
a voluntary or involuntary liquidation, dissolution or winding up of the
Company, or a reduction or decrease in the capital of the Company, without the
adoption of a formal plan of liquidation by the Company.



                                       -3-


     (f) Voting Rights. Except as required by applicable Bermuda law, the
Bye-laws of the Company and as may otherwise be provided herein or in any
amendment hereto, the holders of Preference Shares shall not be entitled to any
voting rights as shareholders of the Company except as follows:

          (1) The affirmative vote of the holders of at least a majority of the
     outstanding Preference Shares, voting with holders of shares of all other
     series of preference shares affected in the same way as a single class, in
     person or by proxy, at a special or annual meeting called for the purpose,
     or by written consent in lieu of a meeting, shall be required to amend,
     repeal or change any provisions of this Schedule in any manner which would
     adversely affect, alter or change the powers, preferences or special rights
     of the Preference Shares and any such securities affected in the same way;
     provided, however, that the creation, authorization or issuance of any
     other class or series of capital shares or the increase or decrease in the
     amount of authorized shares of any such class or series or of the
     Preference Shares, or any increase, decrease or change in the par value of
     any class or series of shares (including the Preference Shares), shall not
     require the consent of the holders of the Preference Shares and shall not
     be deemed to affect adversely, alter or change the powers, preferences and
     special rights of the Preference Shares. With respect to any matter on
     which the holders are entitled to vote as a separate class, each Preference
     Share shall be entitled to one vote.

          (2) Holders of Preference Shares shall be entitled to notice of any
     shareholders' meeting. The holders of Preference Shares shall be entitled
     to vote upon all matters upon which holders of the Common Shares have the
     right to vote, and shall be entitled to the number of votes equal to the
     largest whole number of Common Shares into which such Preference Shares
     could be converted pursuant to the provisions of paragraphs (g)(1) and (h)
     hereof, at the record date for the determination of the shareholders
     entitled to vote on such matters, or, if no such record date is
     established, at the date such vote is taken or any written consent of
     shareholders is solicited, such votes to be counted together with all other
     shares having general voting powers and not separately as a class.

          (3) Notwithstanding the provisions of paragraph (f)(2), the vote of
     the Preference Shares shall be limited as set forth herein.

          (A)  Prior to receipt of the Requisite Shareholder Approval, if the
               votes conferred by the Controlled Shares (as defined in bye-law
               45) of any person, including the Preference Shares held by that
               person, would otherwise represent more than 9.9% of the voting
               power of all shares entitled to vote generally at an election of
               Directors, the vote of each Preference Share held by such person
               shall be reduced by whatever amount is necessary so that after


                                       -4-


               any such reduction, the votes conferred by the Controlled Shares
               of such person, including such Preference Shares, shall
               constitute 9.9% of the total voting power of all shares of the
               Company entitled to vote generally at any election of Directors.

          (B)  Prior to the receipt of the Requisite Nasdaq Approval, if the
               aggregate votes conferred by the Preference Shares then
               outstanding, together with any Common Shares issued upon
               conversion of any Preference Shares, or issued upon exercise of
               any Class A Warrants issued under the Subscription Agreement or
               the Management Subscription Agreement (including by operation of
               the anti-dilution adjustments in the Class A Warrants), or issued
               in cancellation of the Class A Warrants of the Company in
               connection with the transactions under the Subscription Agreement
               (together, the "Aggregate Potential Votes") would exceed 19.9% of
               the total votes entitled to be cast by the Common Shares issued
               and outstanding on November 19, 2001 (the "Total Base Votes"),
               then the vote of each Preference Share shall be reduced
               proportionately (in relation to the total number of Preference
               Shares then outstanding) so that, after giving effect to such
               reduction, the Aggregate Potential Votes do not exceed 19.9% of
               the Total Base Votes (it being understood that if both clause (A)
               and this clause (B) apply, clause (B) shall be applied first,
               then clause (A)).

          (C)  Prior to the receipt of the Requisite Regulatory Approval, if the
               votes conferred by Common Shares and Preference Shares
               beneficially owned by a given person would otherwise represent
               more than 9.9% of the voting power of all shares entitle to vote
               generally at an election of Directors, the vote of each
               Preference Share held by such person shall be reduced by whatever
               amount is necessary so that after any such reduction, the votes
               conferred by the Common Shares and Preference Shares beneficially
               owned by such person, shall constitute 9.9% of the total voting
               power of all shares of the Company entitled to vote generally at
               any election of Directors.

          (D)  Until such time as any waiting period with respect to the
               acquisition of Preference Shares by Orbital Holdings, Ltd. And
               Insurance Private Equity Investors, L.P. required to expire under
               the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as


                                       -5-


               amended, including any extensions thereof, shall have expired or
               been terminated, the Preference Shares held by such GE Purchasers
               shall not have any votes with respect to the election of
               directors.

     (g) Conversion.

     (1) Optional Conversion. Each Preference Share shall be convertible at any
time and from time to time at the option of the holder thereof into fully paid
and nonassessable Common Shares. The number of Common Shares deliverable upon
conversion of a Preference Share as of the Issuance Date, subject to adjustment
as hereinafter provided, shall be one.

     (2) Mandatory Conversion. Following the later of (a) receipt of the
Requisite Shareholder Approval and the Requisite Regulatory Approval, and (b) 90
days after the Fourth Anniversary Adjustment Date, the Preference Shares shall
automatically convert into Common Shares. The number of Common Shares
deliverable upon conversion of a Preference Share shall be as set forth in
paragraphs (g)(1) and (h).

     (3) Fractional Shares. In connection with the conversion of any Preference
Shares, no fractions of Common Shares shall be issued, but in lieu thereof, the
Company shall pay a cash adjustment in respect of such fractional interest in an
amount equal to such fractional interest multiplied by the Current Market Price
of the Common Shares as of the date of conversion. If more than one Preference
Share shall be surrendered for conversion by the same holder at the same time,
the number of full Common Shares issuable on conversion thereof shall be
computed on the basis of the total number of Preference Shares so surrendered.

     (4) Mechanics of Conversion. (a) Before any holder of Preference Shares
shall be entitled to convert the same into Common Shares, he shall surrender the
certificate or certificates therefor, duly endorsed, or deliver an appropriate
indemnity agreement, at the office of the Company or its transfer agent for the
Preference Shares and shall give written notice to the Company of the election
to convert the same and shall state therein the name or names in which the
certificate or certificates for Common Shares are to be issued. The Company
shall, as soon as practicable thereafter, issue and deliver at such office to
such holder of Preference Shares, or to the nominee or nominees of such holder,
a certificate or certificates for the number of Common Shares to which such
holder shall be entitled as aforesaid. A certificate or certificates will be
issued for the remaining Preference Shares in any case in which fewer than all
of the Preference Shares represented by a certificate are converted.



                                       -6-


     (b) In connection with the mandatory conversion, the Company shall deliver
written notice to each such holder that the conversion date has occurred and the
place where certificates are to be surrendered for conversion.

     (5) Issue Taxes. The Company shall pay all issue taxes, if any, incurred in
respect of the issue of Common Shares on conversion. If a holder of shares
surrendered for conversion specifies that the Common Shares to be issued on
conversion are to be issued in a name or names other than the name or names in
which such surrendered shares stand, the Company shall not be required to pay
any transfer or other taxes incurred by reason of the issuance of such Common
Shares to the name of another.

     (6) Reservation of Shares. The Company shall at all times reserve and keep
available, free from preemptive rights, for issuance upon the conversion of
Preference Shares, such number of its authorized but unissued Common Shares as
will from time to time be sufficient to permit the conversion of all outstanding
Preference Shares. Prior to the delivery of any securities which the Company
shall be obligated to deliver upon conversion of the Preference Shares, the
Company shall comply with all applicable laws and regulations which require
action to be taken by the Company. All Common Shares delivered upon conversion
of the Preference Shares will upon delivery be duly and validly issued and fully
paid and nonassessable, free of all liens and charges and not subject to any
preemptive rights.

     (h) Adjustments. The number of Common Shares into which each Preference
Share is convertible shall be subject to adjustment from time to time as
follows:

          (1) Share Splits and Combinations. In case the Company shall at any
     time or from time to time after the Issuance Date (A) subdivide or split
     the outstanding Common Shares, (B) combine or reclassify the outstanding
     Common Shares into a different number of shares or (C) issue by
     reclassification of the Common Shares any shares of the Company, then, and
     in each such case, the number of Common Shares into which each Preference
     Share is convertible shall be adjusted so that the holder of any Preference
     Shares thereafter surrendered for conversion shall be entitled to receive
     the number of Common Shares or other securities of the Company which such
     holder would have owned or have been entitled to receive after the
     occurrence of any of the events described above, had such Preference Shares
     been surrendered for conversion immediately prior to the occurrence of such
     event or the record date therefor, whichever is earlier. An adjustment made
     pursuant to this subparagraph (1) shall become effective at the close of
     business on the day upon which such corporate action becomes effective.
     Such adjustment shall be made successively whenever any event listed above
     shall occur.

          (2) Share Dividends in Common Shares. In case the Company at any time
     or from time to time after the Issuance Date pays a dividend or makes a
     distribution in




                                       -7-


     Common Shares on any class of shares of the Company (other than a dividend
     or distribution of Common Shares or other securities which is made directly
     to the holders of Preference Shares pursuant to paragraph (d), or with
     respect to which adjustments are provided in paragraph (h)(1) above) the
     number of Common Shares into which each Preference Share is convertible
     shall be adjusted so that the holder of any Preference Shares thereafter
     surrendered for conversion shall be entitled to receive the number of
     Common Shares which such holder would have owned or have been entitled to
     receive after such dividend, had such Preference Shares been surrendered
     for conversion immediately prior to the record date for the determination
     of holders entitled to receive such dividend.

          (3) Distribution of Indebtedness, Securities or Assets. In case the
     Company distributes to all holders of Common Shares (whether by dividend or
     other distribution, or in a merger, amalgamation or consolidation or
     otherwise) evidences of indebtedness, shares of any class or series, other
     securities, including rights or warrants to subscribe for securities, cash
     or assets, in each case, of the Company or any of its subsidiaries (other
     than a dividend or distribution which is made directly to the holders of
     Preference Shares pursuant to paragraph (d) above), the Company shall
     distribute to the holders of Preference Shares the same in an amount per
     Preference Share equal to the amount as would be payable with respect to
     the number of Common Share(s) into which such Preference Share is
     convertible pursuant to paragraphs (g)(1) and (h).

          (4) Transactions in Which Common Shares are Exchanged. In case at any
     time the Company shall be a party to any transaction (including, without
     limitation, a merger, amalgamation, consolidation, sale of all or
     substantially all of the Company's assets, liquidation or recapitalization
     of the Common Shares and excluding any transaction to which clauses (1),
     (2) or (3) of this paragraph (h) apply) in which the previously outstanding
     Common Shares shall be changed into or exchanged for different securities
     of the Company or common stock or other securities of another corporation
     or entity (including cash) or any combination of any of the foregoing (each
     such transaction being a "Transaction"), the Company shall make all
     necessary provisions such that each Preference Share shall thereafter be
     convertible into, in lieu of Common Shares, the amount of securities or
     other property to which such holder would actually have been entitled as a
     holder of Common Shares upon the consummation of the Transaction if such
     holder had converted such Preference Shares immediately prior to such
     Transaction (subject to adjustments from and after consummation of the
     Transaction as nearly equivalent as possible to the adjustments provided
     for in this paragraph (h)).

          (5) Below Market Offerings of Common Shares. In case the Company shall
     at any time, or from time to time, issue Common Shares (or securities
     convertible



                                       -8-


     into, or exercisable for, Common Shares) at a price per share (or having a
     conversion or exercise price per share) less than the Current Market Price
     (or, in the case of an issuance or sale in connection with an underwritten
     public offering, less than 99% of the Current Market Price, as determined
     by the underwriters, less underwriting discounts and commissions) as of the
     date of issuance of such shares or of such other securities, then, and in
     each such case, the number of Common Shares into which each Preference
     Share is convertible shall be adjusted so that the holder of each share
     thereof shall be entitled to receive, upon the conversion thereof, the
     number of Common Shares determined by multiplying (A) the number of Common
     Shares into which such share was convertible on the day immediately prior
     to such date by (B) a fraction, the numerator of which shall be the sum of
     (i) the number of Common Shares outstanding on such date and (ii) the
     number of additional Common Shares issued (or into which the other
     securities may convert or be exercised), and the denominator of which shall
     be the sum of (aa) the number of Common Shares outstanding on such date and
     (bb) the number of Common Shares which the aggregate consideration
     receivable by the Company for the total number of Common Shares so issued
     (or into which the other securities may convert or be exercised) would
     purchase at such Current Market Price on such date. An adjustment made
     pursuant to this subparagraph (5) shall be made on the next Business Day
     following the date on which any such issuance is made and shall be
     effective retroactively immediately after the close of business on such
     date. For purposes of this subparagraph (5), the aggregate consideration
     receivable by the Company in connection with the issuance of Common Shares,
     or of other securities convertible into or exercisable for Common Shares,
     shall be deemed to be equal to the sum of the aggregate offering price
     (before deduction of reasonable underwriting discounts or commissions and
     expenses) of all such securities plus the minimum aggregate amount, if any,
     payable upon conversion or exercise of any such other securities into
     Common Shares.

The provisions of this clause (h) shall not apply to the issuance of any Common
Shares (i) pursuant to any restricted share, share option, share purchase or
similar plan or arrangement for the benefit of employees or directors of the
Company or any of its subsidiaries approved by the Board of Directors or a duly
organized committee thereof, (ii) pursuant to options, warrants and conversion
rights outstanding on November 20, 2001, or (iii) issued upon conversion of
Preference Shares or exercise of Class A Warrants issued under the Subscription
Agreement or the Management Subscription Agreement, including pursuant to the
purchase price adjustments therein.

     (i) Certain Definitions. As used in this Schedule, the following terms
shall have the following meanings, unless the context otherwise requires:

     "Board of Directors" means the Board of Directors of the Company.



                                       -9-


     "Business Day" means any day other than a Saturday, Sunday or a United
States federal or Bermuda holiday.

     "Current Market Price" means the average of the closing bid and asked
prices of the Common Shares as reported by the National Association of
Securities Dealers Automated Quotation System, or if the Common Shares are not
there listed, on the principal United States national exchange on which such
shares are listed or admitted.

     "Fourth Anniversary Adjustment Date" means (i) the last date on which an
adjustment could be required to be determined under Section B.3.g. of the
Subscription Agreement or (ii) if such an adjustment is required to be
determined, the date of completion of such adjustment.

     "Issuance Date" means the first date of issuance of any Preference Shares.

     "Management Subscription Agreement" means the Management Subscription
Agreement, dated as of October 24, 2001, by and between the Company and certain
of its officers and directors parties thereto.

     "Requisite Nasdaq Approval" means the approval by the holders of Common
Shares and Preference Shares of the issuance of Common Shares issuable upon
conversion of all Preference Shares issued under the Subscription Agreement and
the Management Subscription Agreement and the issuance of Common Shares issuable
upon exercise of all Class A Warrants issued under the Subscription Agreement
and the Management Subscription Agreement (including by operation of the
anti-dilution adjustments in the Class A Warrants), to the extent that the
number or voting power of all such Common Shares and the 140,380 Common Shares
issued on November 20, 2001 would exceed 19.9% of the total number or the total
voting power of the Common Shares issued and outstanding on November 19, 2001.

     "Requisite Regulatory Approval" means approval by the insurance authorities
in the States of Florida, Missouri, Nebraska and Wisconsin of the acquisition of
greater than 9.9% of the total voting power of all shares of the Company
entitled to vote generally in the election of directors by the "Warburg
Purchasers" and the "H&F Purchasers" (as defined in the Shareholders Agreement)
who are original signatories to the Shareholders Agreement.

     "Requisite Shareholder Approval" means (a) the approval by the holders of
Common Shares and Preference Shares of an amendment to bye-law 45 in the form
included in Exhibit III to the Subscription Agreement and (b) the Requisite
Nasdaq Approval.

     "Shareholders Agreement" means the Shareholders Agreement, dated as of
November 20, 2001, by and between the Company and the shareholders named
therein, as amended from time to time in accordance with its terms.



                                      -10-


     "Subscription Agreement" means the Subscription Agreement, dated as of
October 24, 2001, by and between the Company and each of the Purchasers named
therein, as amended from time to time in accordance with its terms.

     (j) Headings. The headings of the paragraphs of this Schedule are for
convenience of reference only and shall not define, limit or affect any of the
provisions hereof.

     (k) Bye-laws. This Schedule shall be attached to the Bye-laws of the
Company and shall become incorporated in such Bye-laws.