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                               BIOPURE CORPORATION

                                 AGENT'S WARRANT

Warrant No. AW-2                                        Dated: December 14, 2004

      Biopure Corporation, a Delaware corporation (the "COMPANY"), hereby
certifies that, for value received, C.E. Unterberg, Towbin, LLC or its
registered assigns (including permitted transferees, the "HOLDER"), is entitled
to purchase from the Company up to a total of 1,200,000 shares (as adjusted from
time to time as provided in Section 9) 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 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 $0.40 per share (as adjusted from time
to time as provided in Section 9, the "EXERCISE PRICE"), at any time and from
time to time from and after December 14, 2004 (the "INITIAL EXERCISE DATE") to
and including December 14, 2009 (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

            "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

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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 SmallCap Market or Nasdaq National 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.

            "REGISTRATION STATEMENT" means the Company's Registration Statement
on Form S-3 filed with the Commission on June 19, 2003, as such registration
statement is amended or supplemented.

            "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 National 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 9(e)(x)) issued or issuable from time to time upon exercise
of this Warrant.

      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

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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 13, 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 (i) 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 or
(ii) if at any time on or after the Initial Exercise Date the Market Price
exceeds the Exercise Price, by electing a "cashless exercise" of this Warrant by
delivering to the Company, in accordance with Section 13, this Warrant, together
with an Exercise Notice electing such "cashless exercise," in which event the
Company shall issue to the Holder the number of Warrant Shares determined as
follows:

                  X = Y [(A-B)/A]

                  where:

                  X = the number of Warrant Shares to be issued to the Holder
                      upon such cashless exercise;

                  Y = the number of Warrant Shares with respect to which this
                      Warrant is being exercised;

                  A = the Market Price on the Exercise Date; and

                  B = the Exercise Price.

            (d) Notwithstanding anything to the contrary contained herein, the
number of Warrant Shares for which this Warrant may be exercised upon its
exercise by the Holder (or otherwise in respect hereof) shall be limited to the
extent necessary to insure that, following such exercise (or other issuance),
the total number of shares of Common Stock then beneficially

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owned by such Holder and its Affiliates and any other Persons whose beneficial
ownership of Common Stock would be aggregated with the Holder's for purposes of
Section 13(d) of the Exchange Act, does not exceed 4.999% of the total number of
issued and outstanding shares of Common Stock (including for such purpose the
shares of Common Stock issuable upon such exercise). For such purposes,
beneficial ownership shall be determined in accordance with Section 13(d) of the
Exchange Act and the rules and regulations promulgated thereunder. This
provision shall not restrict the number of shares of Common Stock which a Holder
may receive or beneficially own in order to determine the amount of securities
or other consideration that such Holder may receive in the event of a
Fundamental Transaction as contemplated in Section 9 of this Warrant. By written
notice to the Company, the Holder may waive the provisions of this Section 4(d),
but any such waiver will not be effective until the 61st day after delivery of
such notice. For purposes of this section and assisting the calculation required
hereunder, the Company shall provide the Holder, upon two (2) days' prior
written notice, the number of shares of Common Stock outstanding as of the most
recent practicable date.

            (e) Notwithstanding anything to the contrary contained herein, the
number of Warrant Shares for which this Warrant may be exercised upon its
exercise by the Holder (or otherwise in respect hereof) shall be limited to the
extent necessary to insure that, following such exercise (or other issuance),
the total number of shares of Common Stock then beneficially owned by such
Holder and its Affiliates and any other Persons whose beneficial ownership of
Common Stock would be aggregated with the Holder's for purposes of Section 13(d)
of the Exchange Act, does not exceed 9.999% of the total number of issued and
outstanding shares of Common Stock (including for such purpose the shares of
Common Stock issuable upon such exercise). For such purposes, beneficial
ownership shall be determined in accordance with Section 13(d) of the Exchange
Act and the rules and regulations promulgated thereunder. This provision shall
not restrict the number of shares of Common Stock which a Holder may receive or
beneficially own in order to determine the amount of securities or other
consideration that such Holder may receive in the event of a Fundamental
Transaction as contemplated in Section 9 of this Warrant. This restriction may
not be waived. For purposes of this section and assisting the calculation
required hereunder, the Company shall provide the Holder, upon two (2) days'
prior written notice, the number of shares of Common Stock outstanding as of the
most recent practicable date.

            (f) 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.

      5. 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") bearing no restrictive
legends. 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. Failure by the Company to deliver the
Certificate (or to instruct DTC to credit the Holder's balance account with DTC
for the Warrant Shares issuable upon such exercise) on or before the tenth day
following the Exercise Date (the "OUTSIDE DATE")

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shall entitle the Holder to an amount in cash from the Company for each Trading
Day following the Outside Date until the delivery is effected equal to 1.0% of
the product of (i) the Warrant Shares issuable upon such exercise and (ii) the
positive difference between the Market Price on the Outside Date and the
Exercise Price.

            (b) The Warrant and the Warrant Shares will be registered pursuant
to the Registration Statement, and the Company covenants and agrees to maintain
the effectiveness of the Registration Statement until the earlier of (i) such
time as the Warrant Shares have been sold thereunder or (ii) one hundred and
eighty (180) days following the exercise in full of the Warrant or the
expiration of any Warrant Shares not previously exercised thereunder. Not
withstanding the foregoing, in the event that, prior to such time as all of the
Warrant Shares have been sold by the Holder, the Company ceases to be eligible
under the Securities Act of 1933, as amended (the "ACT") or the rules and
regulations promulgated thereunder, to maintain a registration statement on Form
S-3, or in the event that the Warrant or the Warrant Shares cease to be eligible
for inclusion in such Registration Statement to the extent necessary to permit
the Holder to exercise the Warrant and sell the Warrant Shares without
restriction under the Act, the Company will promptly (and in any event within 10
days of the date that the Warrant or any Warrant Shares cease to be so
eligible), amend or file a new registration statement under the Act on a form
eligible for use by the Company for the registration of such securities and use
its best efforts to have such registration statement declared effective by the
Commission as soon as practicable after such filing, which registration
statement shall include such information as may be required to permit the
exercise of the Warrant and the sale of the Warrant Shares without restriction
under the Act. The Holder acknowledges and agrees that the Warrant shall be
exercisable pursuant to any such registration statement only at such times as
the registration statement is effective or in accordance with any applicable
exemption from the registration requirements of the Act. During such time as the
Warrant Shares are registered pursuant to any registration statement under the
Act, the Company further covenants and agrees to make timely filings of all
documents required by be filed under the Act or the Exchange Act in order to
ensure that the registration statement, including the documents incorporated by
reference therein, if any, do not contain an untrue statement of a material fact
or omit to state any material fact required to be stated therein or necessary in
order to make the statements therein not misleading.

            (c) 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.

      6. 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.

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      7. 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.

      8. 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 9 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.

      9. 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 9.

            (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 9(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

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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 9(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 9(e) 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 9; 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 9(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 9(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 9(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:

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            (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
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 9(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 9. The above provisions of this Section 9(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 9,
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 9 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.

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            (h) Adjustments. Notwithstanding any provision of this Section 9, 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 9(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 9, 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 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.

      10. 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 10,
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.

      11. 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.

      12. 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

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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.

      13. 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 13 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.E. Unterberg, Towbin
                                    350 Madison Avenue
                                    New York, NY  10017

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

      14. Warrant Agent. The Company shall serve as warrant agent under this
Warrant. Upon 30 days' 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.

      15. 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 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

                                     -10-
<PAGE>

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:

<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 intends that payment of the Exercise Price shall be made as
      (check one):

              Cash Exercise_______
              Cashless Exercise_______

4.    If the Holder has elected a Cash Exercise, the Holder shall pay the sum of
      $________ to the Company in accordance with the terms of the Warrant.

5.    If the Holder has elected a Cashless Exercise, a certificate shall be
      issued to the Holder for the number of shares equal to the whole number
      portion of the product of the calculation set forth below, which is
      _________. The Company shall pay a cash adjustment in respect of the
      fractional portion of the product of the calculation set forth below in an
      amount equal to the product of the fractional portion of such product and
      the Market Price on the Exercise Day, which product is __________.

              X = Y[(A-B)/A]

              X = the number of Warrant Shares to be issued to the Holder.

              Number of Warrant Shares being exercised: ____________ ("Y").

              Market Price on the Exercise Day: _____________ ("A").

              Exercise Price: _____________("B")

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

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

<PAGE>

Dated: ____________                       Name of Holder:

                                          (Print) ______________________________

                                          By: __________________________________

                                          Title: _______________________________

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

                                       -2-