<PAGE>
                                                                    Exhibit 4.10


THIS WARRANT AND THE SHARES ISSUABLE UPON EXERCISE HEREOF HAVE NOT BEEN
REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "ACT") OR WITH ANY
STATE SECURITIES COMMISSION, AND MAY NOT BE TRANSFERRED OR DISPOSED OF BY THE
HOLDER IN THE ABSENCE OF A REGISTRATION STATEMENT WHICH IS EFFECTIVE UNDER THE
SECURITIES ACT AND APPLICABLE STATE LAWS AND RULES, OR, UNLESS, IMMEDIATELY
PRIOR TO THE TIME SET FOR TRANSFER, SUCH TRANSFER MAY BE EFFECTED WITHOUT
VIOLATION OF THE SECURITIES ACT AND OTHER APPLICABLE STATE LAWS AND RULES.


                               BIOPURE CORPORATION

                                     WARRANT



Warrant No. BW - [*]                                                  Dated: [*]

         Biopure Corporation, a Delaware corporation (the "COMPANY"), hereby
certifies that, for value received, Dawson James Securities, Inc. or its
registered assigns (including permitted transferees, the "HOLDER"), is entitled
to purchase from the Company up to a total of [*] shares (as adjusted from time
to time as provided in Section 10) of Common Stock (as defined below), together
with the associated preferred stock purchase rights under that certain Rights
Agreement (the "RIGHTS AGREEMENT") dated as of September 24, 1999 between the
Company and American Stock Transfer & Trust Company, as rights agent, to the
extent the Rights Agreement is in effect on the date of such purchase, at an
exercise price equal to $[*] per share (as adjusted from time to time as
provided in Section 10, the "EXERCISE PRICE"), at any time and from time to time
from and after February [*], 2007 (the "INITIAL EXERCISE DATE") to and including
August [*], 2011 (the "EXPIRATION DATE"), and subject to the following terms and
conditions.

         1. Definitions. The capitalized terms used herein and not otherwise
defined shall have the meanings set forth below:

                  "AFFILIATE" of any specified Person means any other person or
entity directly or indirectly controlling, controlled by or under direct or
indirect common control with such specified Person. For purposes of this
definition, "CONTROL" means the power to direct the management and policies of
such Person or firm, directly or indirectly, whether through the ownership of
voting securities, by contract or otherwise.

                  "COMMISSION" means the United States Securities and Exchange
Commission.

                  "COMMON STOCK" means the Class A common stock of the Company,
$0.01 par value per share.

                  "ELIGIBLE MARKET" means any of the New York Stock Exchange,
the American Stock Exchange or Nasdaq, and any successor markets thereto.

                  "EXCHANGE ACT" means the Securities Exchange Act of 1934, as
amended.




<PAGE>

                  "MARKET PRICE" shall mean (i) if the principal trading market
for such securities is an exchange, the average of the last reported sale prices
per share for the last ten previous Trading Days in which a sale was reported,
as officially reported on any consolidated tape, (ii) if clause (i) is not
applicable, the average of the closing bid price per share for the last ten
previous Trading Days as set forth by Nasdaq or (iii) if clauses (i) and (ii)
are not applicable, the average of the closing bid price per share for the last
ten previous Trading Days as set forth in the National Quotation Bureau sheet
listing for such securities. Notwithstanding the foregoing, if there is no
reported sales price or closing bid price, as the case may be, on any of the ten
Trading Days preceding the event requiring a determination of Market Price
hereunder, then the Market Price shall be determined in good faith after
reasonable investigation by resolution of the Board of Directors of the Company.

                  "NASDAQ" means the Nasdaq Capital Market or Nasdaq Global
Market, and any successor markets thereto.

                  "OTHER SECURITIES" refers to any capital stock (other than
Common Stock) and other securities of the Company or any other Person which the
Holder of this Warrant at any time shall be entitled to receive, or shall have
received, pursuant to the terms hereof upon the exercise of this Warrant, in
lieu of or in addition to Common Stock.

                  "PERSON" means any court or other federal, state, local or
other governmental authority or other individual or corporation, partnership,
trust, incorporated or unincorporated association, joint venture, limited
liability company, joint stock company, government (or an agency or subdivision
thereof) or other entity of any kind.

                  "TRADING DAY" means (a) any day on which the Common Stock is
listed or quoted and traded on any Eligible Market or (b) if the Common Stock is
not then quoted and traded on any Eligible Market, then a day on which trading
occurs on the Nasdaq Global Market (or any successor thereto).

                  "WARRANT SHARES" shall initially mean shares of Common Stock
(together with the associated preferred stock purchase rights under the Rights
Agreement to the extent the Rights Agreement is in effect on the applicable
date) and in addition may include Other Securities and Substituted Property (as
defined in Section 10(e)(x)) issued or issuable from time to time upon exercise
of this Warrant.



                                      -2-
<PAGE>

         2. Registration of Warrant. The Company shall register this Warrant,
upon records to be maintained by the Company for that purpose (the "WARRANT
REGISTER"), in the name of the record Holder hereof from time to time. The
Company may deem and treat the registered Holder of this Warrant as the absolute
owner hereof for the purpose of any exercise hereof or any distribution to the
Holder, and for all other purposes.

         3. Registration of Transfers. The Company shall register the transfer
of any portion of this Warrant in the Warrant Register, upon surrender of this
Warrant, with the Form of Assignment attached hereto as Appendix A duly
completed and signed, to the Company at its address specified herein. Upon any
such registration and transfer, a new warrant in substantially the form of a
Warrant (any such new warrant, a "NEW WARRANT"), evidencing the portion of this
Warrant so transferred shall be issued to the transferee and a New Warrant
evidencing the remaining portion of this Warrant not so transferred, if any,
shall be issued to the transferring Holder. The acceptance of the New Warrant by
the transferee thereof shall be deemed the acceptance by such transferee of all
of the rights and obligations of a holder of a Warrant.

         4. Exercise and Duration of Warrant.

                  (a) This Warrant shall be exercisable, either in its entirety
         or for a portion of the number of Warrant Shares, by the registered
         Holder at any time and from time to time from and after the Initial
         Exercise Date to and including the Expiration Date. At 5:00 P.M. New
         York City time on the Expiration Date, the portion of this Warrant not
         exercised prior thereto shall be and become void and of no value, and
         the Holder hereof shall have no right to purchase any additional
         Warrant Shares hereunder.

                  (b) A Holder may exercise this Warrant by delivering to the
         Company, in accordance with Section 14, this Warrant, together with (i)
         an exercise notice, in the form attached hereto as Appendix B (the
         "EXERCISE NOTICE"), appropriately completed and duly signed, and (ii)
         payment of the Exercise Price for the number of Warrant Shares as to
         which this Warrant is being exercised (as set forth in Section 4(c)
         below), and the date such items are received by the Company is an
         "EXERCISE DATE." Execution and delivery of an Exercise Notice in
         respect of less than all of the Warrant Shares issuable upon exercise
         of this Warrant shall result in the cancellation of the original
         Warrant and issuance of a New Warrant evidencing the right to purchase
         the remaining number of Warrant Shares.

                  (c) The Holder shall pay the Exercise Price in cash, by
         certified bank check payable to the order of the Company or by wire
         transfer of immediately available funds in accordance with the
         Company's instructions.

                  (d) Except as otherwise provided for herein, this Warrant
         shall not entitle the Holder to any voting rights or other rights as a
         stockholder of the Company by virtue of the ownership hereof.

                  (e) Notwithstanding anything to the contrary herein, after the
         Initial Exercise Date, the Company may, by written notice to the
         Holder, require that the Holder execute and deliver to the Company an
         Exercise Notice exercising all of the Warrant Shares then held by such
         Holder within twenty Business Days of the date of the Company's notice;
         provided, however, that the Company may only provide such notice if the
         daily volume weighted average price per share of the Common Stock for
         each of the ten consecutive


                                      -3-
<PAGE>

         trading days ended immediately prior to the Company's notice is equal
         to or greater than the Exercise Price multiplied by 1.5. At 5:00 P.M.
         New York City time on such 20th Business Day, the portion of this
         Warrant not exercised prior thereto shall be and become void and of no
         value, and the Holder hereof shall have no right to purchase any
         additional Warrant Shares hereunder.

                  (f) The Holder understands that, until such time as the
         Registration Statement has been declared effective or the Warrant
         Shares may be sold pursuant to Rule 144 under the Securities Act
         without any restriction as to the number of securities as of a
         particular date that can then be immediately sold, the certificates
         representing any Warrants Shares issued upon exercise of this Warrant
         will bear a restrictive legend in substantially the following form:

                  "THE SECURITIES EVIDENCED BY THIS CERTIFICATE HAVE NOT BEEN
                  REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE
                  "SECURITIES ACT") OR THE SECURITIES LAWS OF ANY STATE OR OTHER
                  JURISDICTION. THE SECURITIES MAY NOT BE OFFERED, SOLD OR
                  OTHERWISE TRANSFERRED EXCEPT (1) PURSUANT TO AN EXEMPTION FROM
                  REGISTRATION UNDER THE SECURITIES ACT OR (2) PURSUANT TO AN
                  EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT, IN
                  EACH CASE IN ACCORDANCE WITH ALL APPLICABLE SECURITIES LAWS OF
                  THE STATES AND OTHER JURISDICTIONS, AND IN THE CASE OF A
                  TRANSACTION EXEMPT FROM REGISTRATION, UNLESS THE COMPANY HAS
                  RECEIVED AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO IT
                  THAT SUCH TRANSACTION DOES NOT REQUIRE REGISTRATION UNDER THE
                  SECURITIES ACT AND SUCH OTHER APPLICABLE LAWS."

         5. Conversion Right.

                  (a) Determination of Amount. In lieu of the payment of the
         Exercise Price in the manner required by Section 4, the Holder shall
         have the right (but not the obligation) to convert any exercisable but
         unexercised portion of this Warrant into Warrant Shares (the
         "CONVERSION RIGHT") as follows. Upon exercise of the Conversion Right,
         the Company shall deliver to the Holder (without payment by the Holder
         of any of the Exercise Price in cash) that number of Warrant Shares
         equal to the quotient obtained by dividing (x) the "VALUE" (as defined
         below), at the close of trading on the next to last trading day
         immediately preceding the exercise of the Conversion Right, of the
         portion of the Warrant being converted by (y) the "MARKET PRICE" (as
         defined below). The "VALUE" of the portion of the Warrant being
         converted shall equal the remainder derived from subtracting (a) the
         Exercise Price multiplied by the number of Warrant Shares underlying
         that portion of the Warrant being converted from (b) the Market Price
         of the Warrant Shares multiplied by the number of Warrant Shares
         underlying that portion of the Warrant being converted. As used in this
         herein, the term "MARKET PRICE" at any date shall be deemed to be the
         sum of (A) the average last reported sale price of the shares for the
         five trading days ending on the next to last trading day immediately
         preceding the exercise of the Conversion Right as officially reported
         by the principal securities exchange on which the shares are listed or
         admitted to trading, or, if the shares are not listed or admitted to
         trading on any national securities exchange or if any such exchange


                                      -4-
<PAGE>

         on which the shares are listed is not its principal trading market, the
         average last reported sale price for such five trading days as
         furnished by the NASD through the Nasdaq Global Market or Capital
         Market, or, if applicable, the OTC Bulletin Board, or if the shares are
         not listed or admitted to trading on any of the foregoing markets, or
         similar organization, as determined in good faith by resolution of the
         Board of Directors of the Company, based on the best information
         available to it and (B) the intrinsic value of the Warrant using the
         share price determined in (A).

                  (b) Mechanics of Conversion. The Conversion Right may be
         exercised by the Holder on any business day on or after the
         Commencement Date and not later than the Expiration Date by delivering
         the Warrant with a duly executed exercise form attached hereto with the
         Conversion Right section completed to the Company, exercising the
         Conversion Right and specifying the total number of Warrant Shares that
         the Holder will purchase pursuant to such Conversion Right.

         6. Delivery of Warrant Shares.

                  (a) Upon exercise of this Warrant, the Company shall promptly
         issue or cause to be issued and deliver or cause to be delivered to the
         Holder, in such name or names as the Holder may designate, a
         certificate for the Warrant Shares issuable upon such exercise (the
         "CERTIFICATE"). The Holder, or any Person so designated by the Holder
         to receive the Warrant Shares, shall be deemed to have become holder of
         record of such Warrant Shares as of the Exercise Date.

                  (b) This Warrant is exercisable, either in its entirety or,
         from time to time, for a portion of the number of Warrant Shares. Upon
         surrender of this Warrant following one or more partial exercises, the
         Company shall issue or cause to be issued, at its expense, a New
         Warrant evidencing the right to purchase the remaining number of
         Warrant Shares.

         7. Charges, Taxes and Expenses. Issuance and delivery of certificates
for shares of Common Stock upon exercise of this Warrant shall be made without
charge to the Holder for any issue or transfer tax, withholding tax, transfer
agent fee or other incidental tax or expense in respect of the issuance of such
certificates, all of which taxes and expenses shall be paid by the Company;
provided, however, that the Company shall not be required to pay any tax which
may be payable in respect of any transfer involved in the issue, delivery or
registration of any certificates for Warrant Shares or Warrant in a name other
than that of the Holder and that the Holder will be required to pay any tax with
respect to cash received in lieu of fractional shares. The Holder shall be
responsible for all other tax liability that may arise as a result of holding or
transferring this Warrant or receiving Warrant Shares upon exercise hereof.

         8. Replacement of Warrant. If this Warrant is mutilated, lost, stolen
or destroyed, the Company, at the sole expense of the Holder (such expenses, if
any imposed by the Company to be reasonable), shall issue or cause to be issued
in exchange and substitution for and upon cancellation hereof, or in lieu of and
in substitution for this Warrant, a New Warrant, but only upon receipt of
evidence reasonably satisfactory to the Company of such loss, theft or
destruction and customary and reasonable indemnity, if requested by the Company.



                                      -5-
<PAGE>

         9. Reservation of Warrant Shares. The Company covenants that it will at
all times reserve and keep available out of the aggregate of its authorized but
unissued and otherwise unreserved Common Stock, solely for the purpose of
enabling it to issue Warrant Shares upon exercise of this Warrant as herein
provided, the number of Warrant Shares which are then issuable and deliverable
upon the exercise of this entire Warrant, free from all taxes, liens, claims,
encumbrances with respect to the issuance of such Warrant Shares and will not be
subject to any pre-emptive rights or similar rights (taking into account the
adjustments and restrictions of Section 10 hereof). The Company covenants that
all Warrant Shares so issuable and deliverable shall, upon issuance and the
payment of the applicable Exercise Price in accordance with the terms hereof, be
duly and validly authorized, issued, fully paid and nonassessable. The Company
will take all such action as may be necessary to assure that such shares of
Common Stock may be issued as provided herein without violation of any
applicable law or regulation, or of any requirements of any securities exchange
or automated quotation system upon which the Common Stock may be listed or
quoted, as the case may be; provided, however, that such actions shall only
require the Company's best efforts (or other specified standard) to the extent
specifically provided for in this Warrant.

         10. Certain Adjustments. The Exercise Price and number of Warrant
Shares issuable upon exercise of this Warrant are subject to adjustment from
time to time as set forth in this Section 10.

                  (a) Stock Dividends. If the Company, at any time while this
         Warrant is outstanding, pays a dividend on its Common Stock payable in
         additional shares of Common Stock or otherwise makes a distribution on
         any class of capital stock that is payable in shares of Common Stock,
         then in each such case the Exercise Price shall be multiplied by a
         fraction, (A) the numerator of which shall be the number of shares of
         Common Stock outstanding immediately prior to the opening of business
         on the day after the record date for the determination of stockholders
         entitled to receive such dividend or distribution and (B) the
         denominator of which shall be the number of shares of Common Stock
         outstanding immediately after the distribution date of such dividend or
         distribution. Any adjustment made pursuant to this Section 10(a) shall
         become effective immediately after the record date for the
         determination of stockholders entitled to receive such dividend or
         distribution; provided, however, that if following such record date the
         Company rescinds or modifies such dividend or distribution, the
         Exercise Price shall be appropriately adjusted (as of the date that the
         Company effectively rescinds or modifies such dividend or distribution)
         to take into account the effect of such rescinded or modified dividend
         or distribution on the Exercise Price pursuant to this Section 9(a).

                  (b) Stock Splits. If the Company, at any time while this
         Warrant is outstanding, (i) subdivides outstanding shares of Common
         Stock into a larger number of shares, or (ii) combines outstanding
         shares of Common Stock into a smaller number of shares, then in each
         such case the Exercise Price shall be multiplied by a fraction, (A) the
         numerator of which shall be the number of shares of Common Stock
         outstanding immediately before such event and (B) the denominator of
         which shall be the number of shares of Common Stock outstanding
         immediately after such event. Any adjustment pursuant to this Section
         10(b) shall become effective immediately after the effective date of
         such subdivision or combination.

                  (c) Reclassifications. A reclassification of the Common Stock
         (other than any such reclassification in connection with a merger or
         consolidation to which Section 10(e)



                                      -6-
<PAGE>

         applies) into shares of any other class of stock shall be deemed:

               (i)   a distribution by the Company to the holders of its Common
Stock of such shares of such other class of stock for the purposes and within
the meaning of this Section 10; and

               (ii)  if the outstanding shares of Common Stock shall be changed
into a larger or smaller number of shares of Common Stock as part of such
reclassification, such change shall be deemed a subdivision or combination, as
the case may be, of the outstanding shares of Common Stock for the purposes and
within the meaning of Section 10(b).

                  (d) Other Distributions. If the Company, at any time while
         this Warrant is outstanding, distributes to holders of Common Stock (i)
         evidences of its indebtedness, (ii) shares of any class of capital
         stock, (iii) rights or warrants to subscribe for or purchase any shares
         of any class of capital stock or (iv) any other asset, other than a
         distribution of Common Stock covered by Section 10(a), (in each case,
         "DISTRIBUTED PROPERTY"), then in each such case the Exercise Price in
         effect immediately prior to the record date fixed for determination of
         stockholders entitled to receive such distribution (and the Exercise
         Price thereafter applicable) shall be adjusted (effective on and after
         such record date) to equal the product of such Exercise Price
         multiplied by a fraction, (A) the numerator of which shall be Market
         Price on such record date less the then fair market value of the
         Distributed Property distributed in respect of one outstanding share of
         Common Stock, which, if the Distributed Property is other than cash or
         marketable securities, shall be as determined in good faith by the
         Board of Directors of the Company whose determination shall be
         described in a board resolution, and (B) the denominator of which shall
         be the Market Price on such record date; provided, however, that if
         following the record date for such distribution the Company rescinds or
         modifies such distribution, the Exercise Price shall be appropriately
         adjusted (as of the date that the Company effectively rescinds or
         modifies such distribution) to take into account the effect of such
         rescinded or modified distribution on the Exercise Price pursuant to
         this Section 10(d).

                  (e) Fundamental Transactions. If, at any time following the
         Initial Exercise Date, (i) the Company effects any merger or
         consolidation of the Company with or into another Person, (ii) the
         Company effects any sale of all or substantially all of its assets in
         one or a series of related transactions or (iii) there shall occur any
         merger of another Person into the Company whereby the Common Stock is
         cancelled, converted or reclassified into or exchanged for other
         securities, cash or property (in any such case, a "FUNDAMENTAL
         TRANSACTION"), then, as a condition to the consummation of such
         Fundamental Transaction, the Company shall (or, in the case of any
         Fundamental Transaction in which the Company is not the surviving
         entity, the Company shall take all reasonable steps to cause such other
         Person to) execute and deliver to the Holder of this Warrant a written
         instrument providing that:

                      (x)  so long as this Warrant remains outstanding, upon the
exercise hereof at any time on or after the consummation of such Fundamental
Transaction and on such terms and subject to such conditions as shall be nearly
equivalent as may be practicable to the provisions set forth in this Warrant,
this Warrant shall be exercisable into, in lieu of Common Stock issuable upon
such exercise prior to such consummation, the securities or other property (the
"SUBSTITUTED PROPERTY") that would have been received in connection with such
Fundamental Transaction by a holder of the number of shares of Common Stock into
which this


                                      -7-
<PAGE>

Warrant was exercisable immediately prior to such Fundamental Transaction,
assuming such holder of Common Stock:

                           (A) is not a Person with which the Company
consolidated or into which the Company merged or which merged into the Company
or to which such sale or transfer was made, as the case may be (a "CONSTITUENT
PERSON"), or an Affiliate of a Constituent Person; and

                           (B) failed to exercise such Holder's rights of
election, if any, as to the kind or amount of securities, cash and other
property receivable in connection with such Fundamental Transaction (provided,
however, that if the kind or amount of securities, cash or other property
receivable in connection with such Fundamental Transaction is not the same for
each share of Common Stock held immediately prior to such Fundamental
Transaction by a Person other than a Constituent Person or an Affiliate thereof
and in respect of which such rights of election shall not have been exercised (a
"NON-ELECTING SHARE"), then, for the purposes of this Section 10(e), the kind
and amount of securities, cash and other property receivable in connection with
such Fundamental Transaction by each Non-Electing Share shall be deemed to be
the kind and amount so receivable per share by a plurality of the Non-Electing
Shares); and

                      (y)  the rights and obligations of the Company (or, in the
event of a transaction in which the Company is not the surviving Person, such
other Person) and the Holder in respect of Substituted Property shall be as
nearly equivalent as may be practicable to the rights and obligations of the
Company and Holder in respect of Common Stock hereunder.

               Such written instrument shall provide for adjustments which, for
events subsequent to the effective date of such written instrument, shall be as
nearly equivalent as may be practicable to the adjustments provided for in this
Section 10. The above provisions of this Section 10(e) shall similarly apply to
successive Fundamental Transactions.

                  (f) Adjustment of Warrant Shares. Simultaneously with any
         adjustment to the Exercise Price pursuant to paragraphs (a) through (d)
         of this Section 10, the number of Warrant Shares that may be purchased
         upon exercise of this Warrant shall be increased or decreased
         proportionately, so that after such adjustment the aggregate Exercise
         Price payable hereunder for the increased or decreased number of
         Warrant Shares shall be the same as the aggregate Exercise Price
         payable for the Warrant Shares immediately prior to such adjustment.

                  (g) Calculations. All calculations under this Section 10 shall
         be made to the nearest cent or the nearest 1/100th of a share, as
         applicable. The number of shares of Common Stock outstanding at any
         given time shall not include shares owned or held by or for the account
         of the Company, and the disposition of any such shares shall be
         considered an issue or sale of Common Stock.

                  (h) Adjustments. Notwithstanding any provision of this Section
         10, no adjustment of the Exercise Price shall be required if such
         adjustment is less than $0.01; provided, however, that any adjustments
         which by reason of this Section 10(h) are not required to be made shall
         be carried forward and taken into account for purposes of any
         subsequent adjustment required to be made hereunder.

                  (i) Notice of Adjustments. Upon the occurrence of each
         adjustment pursuant to this Section 10, the Company will promptly
         deliver to the Holder a certificate executed by the Company's Chief
         Financial Officer setting forth, in reasonable detail, the event



                                      -8-
<PAGE>

         requiring such adjustment and the method by which such adjustment was
         calculated, the adjusted Exercise Price and the adjusted number or type
         of Warrant Shares or other securities issuable upon exercise of this
         Warrant (as applicable). The Company will retain at its office copies
         of all such certificates and cause the same to be available for
         inspection at said office during normal business hours by the Holder or
         any prospective purchaser of the Warrant designated by the Holder.

                  (j) Notice of Corporate Events. If the Company (i) declares a
         dividend or any other distribution of cash, securities or other
         property in respect of its Common Stock, including, without limitation,
         any granting of rights or warrants to subscribe for or purchase any
         capital stock of the Company or any subsidiary of the Company, (ii)
         authorizes, approves, enters into any agreement contemplating, or
         solicits stockholder approval for, any Fundamental Transaction or (iii)
         authorizes the voluntary dissolution, liquidation or winding up of the
         affairs of the Company, then the Company shall deliver to the Holder a
         notice describing the material terms and conditions of such transaction
         at least 15 calendar days prior to the applicable record or effective
         date on which a Person would need to hold Common Stock in order to
         participate in or vote with respect to such transaction, and the
         Company will take all steps reasonably necessary in order to ensure
         that the Holder is given the practical opportunity to exercise this
         Warrant prior to such time so as to participate in or vote with respect
         to such transaction; provided, however, that the failure to deliver
         such notice or any defect therein shall not affect the validity of the
         corporate action required to be described in such notice.

         11. Fractional Shares. The Company shall not be required to issue or
cause to be issued fractional Warrant Shares on the exercise of this Warrant. If
any fraction of a Warrant Share would, except for the provisions of this Section
11, be issuable upon exercise of this Warrant, the Company shall make a cash
payment to the Holder equal to (a) such fraction multiplied by (b) the Market
Price on the Exercise Date of one full Warrant Share.

         12. Listing on Securities Exchanges. The Company has listed, and will
use its best efforts to maintain the listing of, the Warrant Shares on Nasdaq.
In furtherance and not in limitation of any other provision of this Warrant, if
the Company at any time shall list any Common Stock on any Eligible Market other
than Nasdaq, the Company will, at its expense, simultaneously list the Warrant
Shares (and use its best efforts to maintain such listing) on such Eligible
Market, upon official notice of issuance following the exercise of this Warrant;
and the Company will so list, register and use its best efforts to maintain such
listing on any Eligible Market any Other Securities, if and at the time that any
securities of like class or similar type shall be listed on such Eligible Market
by the Company.

         13. Remedies. The Company stipulates that the remedies at law of the
Holder of this Warrant in the event of any default or threatened default by the
Company in the performance of or compliance with any of the terms of this
Warrant are not and will not be adequate, and that such terms may be
specifically enforced by a decree for the specific performance of any agreement
contained herein or by an injunction against a violation of any of the terms
hereof or otherwise.



                                      -9-
<PAGE>

         14. Notices. Any and all notices or other communications or deliveries
hereunder (including without limitation any Exercise Notice) shall be in writing
and shall be mailed by certified mail, return receipt requested, or by a
nationally recognized courier service or delivered (in person or by facsimile),
against receipt to the party to whom such notice or other communication is to be
given. Any notice or other communication given by means permitted by this
Section 14 shall be deemed given at the time of receipt thereof. The address for
such notices or communications shall be as set forth below:

         If to the Company:  Biopure Corporation
                             11 Hurley Street
                             Cambridge, MA 02141

         If to the Holder:   c/o Biopure Corporation
                             11 Hurley Street
                             Cambridge, MA 02141

Or such other address as is provided to such other party in accordance with this
Section 14.

         15. Warrant Agent. The Company shall serve as warrant agent under this
Warrant. Upon a prompt written notice to the Holder, the Company may appoint a
new warrant agent. Any Person into which any new warrant agent may be merged,
any Person resulting from any consolidation to which any new warrant agent shall
be a party or any Person to which any new warrant agent transfers substantially
all of its corporate trust or shareholders services business shall be a
successor warrant agent under this Warrant without any further act. Any such
successor warrant agent shall promptly cause notice of its succession as warrant
agent to be mailed (by first class mail, postage prepaid) to the Holder at the
Holder's last address as shown on the Warrant Register.

         16. Registration Rights. The Common Stock issuable upon exercise of
this Warrant shall constitute Registrable Securities (as such term is defined in
the Securities Purchase Agreement of even date herewith between the Holder and
the Company (the "SECURITIES PURCHASE AGREEMENT")). The original Holder of this
Warrant, and any valid transferees thereof pursuant to the Securities Purchase
Agreement, shall be entitled to all of the benefits afforded to a holder of any
Registrable Securities under the Securities Purchase Agreement and such holder,
by its acceptance of this Warrant, agrees to be bound by and to comply with the
terms and conditions of the Securities Purchase Agreement applicable to the
holder as a holder of Registrable Securities.

         17. Miscellaneous. (a) This Warrant may be assigned by the Holder. This
Warrant may not be assigned by the Company, except to a successor in the event
of a Fundamental Transaction. This Warrant shall be binding on and inure to the
benefit of the parties hereto and their respective successors and assigns.
Subject to the preceding sentence, nothing in this Warrant shall be construed to
give to any Person other than the Company and the Holder any legal or equitable
right, remedy or cause of action under this Warrant. This Warrant may be amended
only in writing signed by the Company and the Holder and their successors and
assigns.

                  (b) The Company will not, by amendment of its governing
         documents or through any reorganization, transfer of assets,
         consolidation, merger, dissolution, issue or sale of securities or any
         other voluntary action, avoid or seek to avoid the observance or



                                      -10-
<PAGE>

         performance of any of the terms of this Warrant, but will at all times
         in good faith assist in the carrying out of all such terms and in the
         taking of all such action as may be necessary or appropriate in order
         to protect the rights of the Holder against impairment. Without
         limiting the generality of the foregoing, the Company (i) will not
         increase the par value of any Warrant Shares above the amount payable
         therefor upon exercise thereof, and (ii) will take all such action as
         may be reasonably necessary or appropriate in order that the Company
         may validly and legally issue fully paid and nonassessable Warrant
         Shares on the exercise of this Warrant, free from all taxes, liens,
         claims and encumbrances and (iii) will not close its shareholder books
         or records in any manner which interferes with the timely exercise of
         this Warrant.

                  (c) This Warrant shall be governed by and construed and
         enforced in accordance with the laws of the State of New York. Each
         party hereby irrevocably submits to the exclusive jurisdiction of the
         state and Federal courts sitting in the City of New York, Borough of
         Manhattan, for the adjudication of any dispute hereunder or in
         connection herewith or with any transaction contemplated hereby or
         discussed herein, and hereby irrevocably waives, and agrees not to
         assert in any suit, action or proceeding that it is not personally
         subject to the jurisdiction of any such court or that such suit, action
         or proceeding is improper. Each party hereby irrevocably waives
         personal service of process and consents to process being served in any
         such suit, action or proceeding by mailing a copy thereof via
         registered or certified mail or overnight delivery (with evidence of
         delivery) to such party at the address in effect for notices to it
         under this Warrant and agrees that such service shall constitute good
         and sufficient service of process and notice thereof. Nothing contained
         herein shall be deemed to limit in any way any right to serve process
         in any manner permitted by law. THE PARTIES HEREBY WAIVE ALL RIGHTS TO
         A TRIAL BY JURY.

                  (d) Neither party shall be deemed in default of any provision
         of this Warrant, to the extent that performance of its obligations or
         attempts to cure a breach hereof are delayed or prevented by any event
         reasonably beyond the control of such party, including, without
         limitation, war, hostilities, acts of terrorism, revolution, riot,
         civil commotion, national emergency, strike, lockout, unavailability of
         supplies, epidemic, fire, flood, earthquake, force of nature,
         explosion, embargo, or any other Act of God, or any law, proclamation,
         regulation, ordinance, or other act or order of any court, government
         or governmental agency, provided that such party gives the other party
         written notice thereof promptly upon discovery thereof and uses
         reasonable efforts to cure or mitigate the delay or failure to perform.

                  (e) The headings herein are for convenience only, do not
         constitute a part of this Warrant and shall not be deemed to limit or
         affect any of the provisions hereof.

                  (f) In case any one or more of the provisions of this Warrant
         shall be deemed invalid or unenforceable in any respect, the validity
         and enforceability of the remaining terms and provisions of this
         Warrant shall not in any way be affected or impaired thereby and the
         parties will attempt in good faith to agree upon a valid and
         enforceable provision which shall be a commercially reasonable
         substitute therefor, and upon so agreeing, shall incorporate such
         substitute provision in this Warrant.


                  [Remainder of page intentionally left blank,
                             signature page follows]


                                      -11-
<PAGE>


         IN WITNESS WHEREOF, the Company has caused this Warrant to be duly
executed by its authorized officer as of the date first indicated above.

                                         BIOPURE CORPORATION




                                         By:
                                             -----------------------------------
                                             Name:
                                             Title:















                            [PLACEMENT AGENT WARRANT]

<PAGE>





                                   APPENDIX A

                               FORM OF ASSIGNMENT

           (to be completed and signed only upon transfer of Warrant)

         FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfers
unto ____________________ the right represented by the within Warrant to
purchase _____________ shares of Common Stock of Biopure Corporation to which
the within warrant relates and appoints __________________________ attorney to
transfer said right on the books of Biopure Corporation with full power of
substitution in the premises.


Dated:
      ----------------                  ----------------------------------------
                                        (Signature must conform in all respects
                                        to name of Holder as specified on face
                                        of the Warrant)

                                        Address of Transferee:

                                        ----------------------------------------

                                        ----------------------------------------

                                        ----------------------------------------

In the presence of:


--------------------------------



<PAGE>



                                   APPENDIX B

                             FORM OF EXERCISE NOTICE

(To be executed by the Holder to exercise the right to purchase shares of Common
Stock under the foregoing Warrant)

To:      Biopure Corporation

The undersigned is the Holder of Warrant No. [ ] (the "Warrant") issued by
Biopure Corporation, a Delaware corporation (the "Company"). Capitalized terms
used herein and not otherwise defined have the respective meanings set forth in
the Warrant.

1.       The Warrant is currently exercisable to purchase a total of _________
         Warrant Shares.

2.       The undersigned Holder hereby exercises its right to purchase _________
         Warrant Shares pursuant to the Warrant.

3.       The Holder shall pay the sum of $________ to the Company in accordance
         with the terms of the Warrant.

4.       Pursuant to this exercise, the Company shall deliver to the Holder
         Warrant Shares in accordance with the terms of the Warrant.

5.       Following this exercise, the Warrant shall be exercisable to purchase a
         total of __________ Warrant Shares.



Dated:                                  Name of Holder:
       ---------------

                                        (Print)
                                                --------------------------------

                                        By:
                                            ------------------------------------

                                        Title:
                                               ---------------------------------
                                        (Signature must conform in all respects
                                        to name of Holder as specified on face
                                        of the Warrant)