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                                                                     EXHIBIT 3.4

                       INTRABIOTICS PHARMACEUTICALS, INC.

                           CERTIFICATE OF DESIGNATION
                                       OF
                      SERIES A CONVERTIBLE PREFERRED STOCK

                         (PURSUANT TO SECTION 151 OF THE
                        DELAWARE GENERAL CORPORATION LAW)

     INTRABIOTICS PHARMACEUTICALS, INC., a corporation organized and existing
under the laws of the State of Delaware (the "CORPORATION"), in accordance with
the provisions of Section 151 of the Delaware General Corporation Law, DOES
HEREBY CERTIFY:

     That pursuant to the authority conferred upon the Board of Directors of the
Corporation (the "BOARD OF DIRECTORS") by the Certificate of Incorporation of
the Corporation and by Section 151(g) of the Delaware General Corporation Law,
on January 27, 2003, the Board of Directors adopted the following resolutions,
creating a series of shares of convertible Preferred Stock, designated as
"Series A Convertible Preferred Stock:"

          "RESOLVED, that pursuant to the authority vested in the Board of
     Directors of INTRABIOTICS PHARMACEUTICALS, INC., a corporation organized
     and existing under the laws of the State of Delaware by the Certificate of
     Incorporation of the Corporation (the "CERTIFICATE OF INCORPORATION"), the
     Board of Directors does hereby provide for the authorization and issuance
     of a series of convertible Preferred Stock, par value $.001 per share, of
     the Corporation, to be designated "Series A Convertible Preferred Stock,"
     initially consisting of 350 shares, and does hereby fix and herein state
     and express the designations, powers, preferences, and relative
     participating, optional, or other special rights, and the qualifications,
     limitations, and restrictions thereof, as follows:

     Section 1. Designation and Amount. Three hundred fifty (350) shares of
Preferred Stock are designated Series A Convertible Preferred Stock (the "SERIES
A PREFERRED"), with the rights, preferences, privileges and restrictions
specified herein.

     Section 2. Dividends. Holders of the Series A Preferred shall be entitled
to the following dividend rights:

          a.   Series A Dividends. Holders of Series A Preferred on the
applicable Dividend Record Date (as defined below), in preference to the holders
of any other stock of the Corporation ranking junior in right of payment of
dividends, including, without limitation, the Corporation's Common Stock (the
"COMMON STOCK") (stock of the Corporation being junior to the Series A Preferred
with respect to voting, dividends or liquidation preferences, as the case may
be, being referred to herein as "JUNIOR STOCK"), shall be entitled to receive,
but only out of funds that are legally available therefor, cumulative dividends,
payable quarterly on March 31, June 30, September 30 and December 31 of each
year commencing on June 30, 2003 (each such date being referred to herein as a
"DIVIDEND PAYMENT DATE"), at the rate of eight percent (8%) per annum of the
Original Issue Price (as defined below) on each outstanding share of Series A
Preferred (as adjusted for any stock dividends, combinations, splits,
recapitalizations and the like

                                       1.
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with respect to such shares), in the form of shares of Common Stock. The number
of shares of Common Stock issuable to each holder of Series A Preferred shall be
equal to the quotient obtained by dividing the aggregate amount of dividends
such holder is entitled to receive by the per share Computed Price (as defined
below). The Corporation shall, in lieu of issuing any fractional shares, pay
cash to such holders for such fractional shares. The "ORIGINAL ISSUE PRICE" of
the Series A Preferred shall be $10,000.00. The "DIVIDEND RECORD DATE" shall
mean, with respect to any Dividend Payment Date, the date that is ten (10)
business days prior to such Dividend Payment Date. The "COMPUTED PRICE" of one
share of Common Stock shall mean the average of the closing sale prices (or the
closing bids, if no sales were reported) of the Common Stock on The Nasdaq
National Market, if the Common Stock is traded on such market, for the five (5)
trading days immediately preceding and ending on the last trading day prior to
the applicable Dividend Payment Date. If the Common Stock is not traded on The
Nasdaq National Market, the Computed Price shall be determined by reference to
the closing sale prices (or the closing bids, if no sales were reported) of the
Common Stock on the Nasdaq SmallCap Market, OTC Bulletin Board, Pink Sheets or
on any other exchange on which the Common Stock is listed or traded, whichever
is applicable. In the absence of such markets for the Common Stock, the Computed
Price shall be determined in good faith by the Board of Directors.

               b. Limitations on Dividends. So long as any shares of Series A
Preferred are outstanding, the Corporation shall not pay or declare any
dividend, whether in cash or property, or make any other distribution on Junior
Stock, or purchase, redeem or otherwise acquire for value any shares of Junior
Stock unless and until all accrued or declared and unpaid dividends on the
Series A Preferred shall have first been paid or declared and set apart;
provided, however, that the foregoing shall not be deemed to prohibit the
repurchase of shares of Common Stock from employees, officers, directors,
consultants or other persons performing services for the Corporation or any
subsidiary pursuant to agreements under which the Corporation has the option to
repurchase such shares at cost upon the occurrence of certain events, such as
the termination of employment, or through the exercise of any right of first
refusal.

     In the event that the payment of dividends in the form of shares of Common
Stock as provided for in Section 2(a) above would cause (A) a holder of Series A
Preferred to beneficially own (as that term is defined in Rule 13d-3 of the
Securities Exchange Act of 1934, as amended (the "EXCHANGE ACT")) in excess of
19.9% of the Corporation's Common Stock (treating outstanding shares of Series A
Preferred as if converted) outstanding as of the applicable Dividend Record Date
or (B) the total number of shares issued or deemed issued under the Preferred
Stock and Warrant Purchase Agreement dated February ___, 2003, pursuant to which
shares of Series A Preferred are being sold and issued (the "PURCHASE
AGREEMENT"), to exceed 19.9% of the Corporation's issued and outstanding shares
of Common Stock on the date of the Purchase Agreement without first obtaining
stockholder approval (in accordance with the requirements of The Nasdaq Stock
Market for purposes of Rule 4350(i)(1)(B) or Rule 4350(i)(1)(D) thereof, as
applicable), then the Corporation shall not pay such dividends and such
dividends shall accrue and be paid at the earliest time, and from time to time,
on which the Corporation is legally able to pay such dividends without violating
the applicable requirements of The Nasdaq Stock Market.

               c. Common Stock Dividends. In the event dividends are paid on any
share of Common Stock, other than in the form of shares of Common Stock pursuant
to Section 4.f, the

                                       2.
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Corporation shall pay an additional dividend on all outstanding shares of Series
A Preferred in a per share amount equal (on an as-if-converted to Common Stock
basis) to the amount paid or set aside for each share of Common Stock.

               d. Waiver. The holders of the Series A Preferred expressly waive
their rights, if any, as described in California Corporations Code Sections 502,
503 and 506 as they relate to repurchases of shares of Common Stock upon
termination of employment or service as a consultant or director.

     Section 3. Liquidation Rights.

          a.   Upon any liquidation, dissolution, or winding up of the
Corporation, whether voluntary or involuntary (a "LIQUIDATION EVENT"), before
any distribution or payment shall be made to the holders of any Junior Stock,
each holder of Series A Preferred shall be entitled to be paid out of the assets
of the Corporation legally available for distribution, or the consideration
received in such transaction, an amount per share of Series A Preferred equal to
the Original Issue Price plus all accrued or declared and unpaid dividends, such
and only such dividends to be payable in cash, on the Series A Preferred, if
any, (as adjusted for any stock dividends, combinations, splits,
recapitalizations and the like with respect to such shares after the date that
shares of Series A Preferred are first issued (the "ORIGINAL ISSUE DATE")) for
each share of Series A Preferred held by such holder. If, upon any such
liquidation, dissolution or winding up, the assets of the Corporation (or the
consideration received in such transaction) shall be insufficient to make
payment in full to all holders of Series A Preferred of the liquidation
preference set forth in this Section 3.a, then such assets (or consideration)
shall be distributed among the holders of the Series A Preferred at the time
outstanding, ratably in proportion to the full amounts to which they would
otherwise be respectively entitled. After payment of the full liquidation
preference of the Series A Preferred as aforesaid, the assets of the Corporation
legally available for distribution (or the consideration received in such
transaction), if any, shall be distributed to the holders of any Junior Stock in
accordance with the Certificate of Incorporation and any other Certificate of
Designations creating a series of Preferred Stock or any similar stock.

          b.   Deemed Liquidation.

               (i)  For purposes of Section 3.a, the holders of not less than a
majority of the then outstanding Series A Preferred may elect to have treated as
a Liquidation Event: (A) the acquisition of the Corporation by another entity by
means of any transaction or series of related transactions that have been
approved by the Board of Directors of the Corporation (including, without
limitation, any reorganization, merger or consolidation, other than with a
wholly-owned subsidiary corporation or solely for the purposes of changing the
domicile of the Corporation), or (B) a sale, transfer or disposition of all or
substantially all of the shares or assets of the Corporation by a means of any
transaction or series of related transactions that have been approved by the
Board of Directors of the Corporation (including, without limitation, any
reorganization, merger or consolidation, other than with a wholly-owned
subsidiary corporation or solely for the purposes of changing the domicile of
the Corporation); unless the Corporation's stockholders as constituted
immediately prior to such transaction will, immediately after such

                                       3.
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transaction (by virtue of securities issued as consideration for the
transaction) hold at least fifty percent (50%) of the voting power of the
surviving or acquiring entity.

               (ii) In the event of an election made pursuant to Section 3.b(i),
the value of any non-cash consideration received by the Corporation will be
deemed to be its fair market value (as determined in good faith by the Board of
Directors). Any securities to be delivered to the holders of Series A Preferred
or Common Stock, as the case may be, shall be valued as follows:

                    (A) Securities not subject to investment letter or other
similar restrictions on free marketability:

                         1) If traded on a securities exchange or through The
Nasdaq National Market, the value shall be deemed to be the average of the
closing prices of the securities on such exchange over the thirty (30) trading
days ending three (3) trading days prior to the closing;

                         2) If actively traded over-the-counter, the value shall
be deemed to be the average of the closing bid or sale prices (whichever is
applicable) over the thirty (30) trading days ending three (3) trading days
prior to the closing; and

                         3) If there is no active public market, the value shall
be the fair market value thereof (as determined in good faith by the Board of
Directors).

                    (B)  The method of valuation of securities subject to
investment letter or other restrictions on free marketability (other than
restrictions arising solely by virtue of a stockholder's status as an affiliate
or former affiliate) shall be to make an appropriate discount from the market
value determined as above in A(1), (2) or (3) to reflect the approximate fair
market value thereof, as mutually determined in good faith by the Board of
Directors and the holders of at least two-thirds (2/3) of the Series A Preferred
then outstanding provided that if the Board of Directors and the holders of at
least two-thirds (2/3) of the Series A Preferred then outstanding are unable to
reach agreement, then by independent appraisal by a mutually agreed to
investment banker, the fees of which shall be paid by the Corporation.

               (iii) In the event the requirements of this Section 3 are not
complied with, the Corporation shall either:

                    (A) cause such closing to be postponed until such time as
the requirements of this Section 3 have been complied with; or

                    (B) cancel such transaction, in which event the respective
rights, preferences and privileges of the holders of Series A Preferred shall
revert to and be the same as such rights, preferences and privileges existing
immediately prior thereto.

     Section 4. Conversion. The holders of the Series A Preferred shall have
conversion rights as follows:

                                       4.
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          a.   Optional Conversion. Subject to and in compliance with the
provisions of this Section 4, any shares of Series A Preferred may, at the
option of the holder, be converted at any time into fully-paid and nonassessable
shares of Common Stock. The number of shares of Common Stock to which a holder
of Series A Preferred shall be entitled upon conversion shall be the product
obtained by multiplying the Conversion Rate then in effect (determined as
provided in Section 4.b below) by the number of shares of Series A Preferred
being converted.

          b.   Conversion Rate. The Conversion Rate for Series A Preferred in
effect at any time for conversion of the Series A Preferred (the "CONVERSION
RATE") shall be the quotient obtained by dividing the Original Issue Price by
the Conversion Price, calculated as provided in Section 4(c) below.

          c.   Conversion Price. The Conversion Price for the Series A Preferred
shall initially be equal to ninety-two percent (92%) of the Closing Price (as
defined below) (the "CONVERSION PRICE"). Such initial Conversion Price shall be
adjusted from time to time in accordance with this Section 4. All references to
the Conversion Price herein shall mean the Conversion Price as so adjusted. The
"CLOSING PRICE" shall be the lesser of (i) the average of the closing sale
prices (or the closing bids, if no sales were reported) of the Common Stock as
reported on The Nasdaq National Market for the five (5) trading days immediately
preceding and ending on the last trading day prior to the date of execution of
the Purchase Agreement and (ii) the average of the closing sale prices (or the
closing bids, if no sales were reported) of the Common Stock as reported on The
Nasdaq National Market for the five (5) trading days immediately preceding and
ending on the last trading day prior to the date of the Company's stockholders
meeting at which the issuance of the Series A Preferred is approved; provided,
however, that if the Corporation has not effected a reverse stock split of the
Corporation's outstanding Common Stock within the range of 1-for-8 to 1-for 12
(the "Reverse Split") at least three (3) trading days prior to the beginning of
the five (5) trading day range described in clause (ii) immediately above, then
such five (5) trading day range shall not commence until the date that is the
fourth trading day after the effectiveness of the Reverse Split.

          d.   Mechanics of Conversion. Each holder of Series A Preferred who
desires to convert the same into shares of Common Stock pursuant to this Section
4 shall surrender its certificate or certificates therefor, duly endorsed, at
the office of the Corporation or of any transfer agent for the Series A
Preferred, and shall give written notice to the Corporation at such office that
it elects to convert the same. Such notice shall state the number of shares of
Series A Preferred being converted. Thereupon, the Corporation shall promptly
issue and deliver at such office to such holder of Series A Preferred a
certificate or certificates, registered in such names as are specified by the
holder, for the number of shares of Common Stock to which such holder is
entitled and shall promptly pay in cash (at the Common Stock's fair market value
determined by the Board of Directors as of the date of conversion) the value of
any fractional share of Common Stock otherwise issuable to any holder of Series
A Preferred. In lieu of delivering physical certificates representing the Common
Shares issuable upon conversion of Series A Preferred or in payment of dividends
hereunder, provided the Corporation's transfer agent is participating in the
Depository Trust Company ("DTC") Fast Automated Securities Transfer ("FAST")
program, upon request of the holder, and in accordance with applicable law, the
Corporation shall use its reasonable best efforts to cause its transfer agent to
electronically transmit the Common Shares issuable upon conversion or dividend
payment to the holder, by

                                       5.
<PAGE>

crediting the account of the holder's prime broker with DTC through its Deposit
Withdrawal Agent Commission ("DWAC") system. The parties agree to coordinate
with DTC to accomplish this objective. Such conversion shall be deemed to have
been made at the close of business on the date of such surrender of the
certificates representing the shares of Series A Preferred to be converted, and
the person or persons entitled to receive the shares of Common Stock issuable
upon such conversion shall be treated for all purposes as the record holder or
holders of such shares of Common Stock on such date.

          e.   Adjustment for Stock Splits and Combinations. If at any time or
from time to time after the Original Issue Date the Corporation effects a
subdivision of the outstanding Common Stock without a corresponding subdivision
of the Series A Preferred, the Conversion Price in effect immediately before
that subdivision shall be proportionately decreased. Conversely, if at any time
or from time to time after the Original Issue Date the Corporation combines the
outstanding shares of Common Stock into a smaller number of shares without a
corresponding combination of the Series A Preferred, the Conversion Price in
effect immediately before the combination shall be proportionately increased.
Any adjustment under this Section 4.e shall become effective at the close of
business on the date the subdivision or combination becomes effective.

          f.   Adjustment for Common Stock Dividends and Distributions. If at
any time or from time to time after the Original Issue Date the Corporation pays
a dividend or other distribution to the holders of Common Stock (without a
corresponding payment to the holders of Series A Preferred) in additional shares
of Common Stock, the Conversion Price that is then in effect shall be decreased
as of the time of such issuance, as provided below:

               (i) The Conversion Price shall be adjusted by multiplying the
Conversion Price then in effect by a fraction equal to:

                    (A) the numerator of which is the total number of shares of
Common Stock issued and outstanding immediately prior to the time of such
issuance, and

                    (B) the denominator of which is the total number of shares
of Common Stock issued and outstanding immediately prior to the time of such
issuance plus the number of shares of Common Stock issuable in payment of such
dividend or distribution;

               (ii) If the Corporation fixes a record date to determine which
holders of Common Stock are entitled to receive such dividend or other
distribution, the Conversion Price shall be fixed as of the close of business on
such record date and the number of shares of Common Stock shall be calculated
immediately prior to the close of business on such record date; and

               (iii) If such record date is fixed and such dividend is not fully
paid or if such distribution is not fully made on the date fixed therefor, the
Conversion Price shall be recomputed accordingly as of the close of business on
such record date and thereafter the Conversion Price shall be adjusted pursuant
to this Section 4.f to reflect the actual payment of such dividend or
distribution.

                                       6.
<PAGE>


          g.   Adjustment for Reclassification, Exchange and Substitution. If at
any time or from time to time after the Original Issue Date, the Common Stock
issuable upon the conversion of the Series A Preferred is changed into the same
or a different number of shares of any class or classes of stock, whether by
recapitalization, reclassification or otherwise (other than a subdivision or
combination of shares or stock dividend or a reorganization, merger,
consolidation or sale of assets provided for elsewhere in this Section 4), in
any such event each holder of Series A Preferred shall then have the right to
convert such stock into the kind and amount of stock and other securities and
property receivable upon such recapitalization, reclassification or other change
by holders of the maximum number of shares of Common Stock into which such
shares of Series A Preferred could have been converted immediately prior to such
recapitalization, reclassification or change, all subject to further adjustment
as provided herein or with respect to such other securities or property by the
terms thereof.

          h.   Reorganizations, Mergers or Consolidations. If at any time or
from time to time after the Original Issue Date, there is a capital
reorganization of the Common Stock or the merger or consolidation of the
Corporation with or into another corporation or another entity or person or the
sale, lease or other disposition of all or substantially all of the assets of
the Corporation (an "ASSET TRANSFER") (other than a recapitalization,
subdivision, combination, reclassification, exchange or substitution of shares
provided for elsewhere in this Section 4) (a "CAPITAL REORGANIZATION"), as a
part of such Capital Reorganization, provision shall be made so that each holder
of Series A Preferred shall thereafter be entitled to receive upon conversion of
the Series A Preferred the kind and amount of stock and other securities and
property receivable upon such Capital Reorganization by holders of the maximum
number of shares of Common Stock into which such shares of Series A Preferred
could have been converted immediately prior to such Capital Reorganization, all
subject to further adjustment as provided herein or with respect to such other
securities or property by the terms thereof. In any such case, appropriate
adjustment shall be made in the application of the provisions of this Section 4
with respect to the rights of the holders of Series A Preferred after the
Capital Reorganization to the end that the provisions of this Section 4
(including adjustment of the Conversion Price then in effect and the number of
shares issuable upon conversion of the Series A Preferred) shall be applicable
after that event and be as nearly equivalent as practicable.

          i.   Ownership Limitation. In the event that the effect of any
provision set forth in this Section 4 would cause (A) a holder of Series A
Preferred to beneficially own (as that term is defined in Rule 13d-3 of the
Exchange Act) in excess of 19.9% of the Corporation's Common Stock (treating
outstanding shares of Series A Preferred as if converted) outstanding as of the
applicable effective date or (B) the total number of shares issued or deemed
issued under the Purchase Agreement would exceed 19.9% of the Corporation's
issued and outstanding shares of Common Stock on the date of the Purchase
Agreement without first obtaining stockholder approval (in accordance with the
requirements of The Nasdaq Stock Market for purposes of Rule 4350(i)(1)(B) or
Rule 4350(i)(1)(D) thereof, as applicable), then the Corporation shall not be
required to take any action or make any adjustment with respect to the Series A
Preferred until such time as such action could be taken or such adjustment could
be made without the violation of applicable requirements of The Nasdaq Stock
Market.

          j.   No Impairment. Without the consent of the holders of the then
outstanding Series A Preferred as required under Section 5.c, the Corporation
will not, by

                                       7.
<PAGE>

amendment of its Certificate of Incorporation 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 to be observed or performed hereunder by the
Corporation, but will at all times in good faith assist in the carrying out of
all the provisions of Section 4 and in the taking of all such action as may be
necessary or appropriate in order to protect the conversion rights of the
holders of Series A Preferred against impairment.

          k.   Certificate of Adjustment. In each case of an adjustment or
readjustment of the Conversion Price for the number of shares of Common Stock or
other securities issuable upon conversion of the Series A Preferred, if the
Series A Preferred is then convertible pursuant to this Section 4, the
Corporation, at its expense, shall compute such adjustment or readjustment in
accordance with the provisions hereof and prepare a certificate showing such
adjustment or readjustment, and shall mail such certificate, by first class
mail, postage prepaid, to each registered holder of Series A Preferred at the
holder's address as shown in the Corporation's books. The certificate shall set
forth such adjustment or readjustment, showing in detail the facts upon which
such adjustment or readjustment is based, including a statement of (i) the
Conversion Price at the time in effect and (ii) the type and amount, if any, of
other property which at the time would be received upon conversion of the Series
A Preferred.

          l.   Notices of Record Date. Upon (i) any taking by the Corporation of
a record of the holders of any class of securities for the purpose of
determining the holders thereof who are entitled to receive any dividend or
other distribution, or (ii) any capital reorganization of the Corporation, any
reclassification or recapitalization of the capital stock of the Corporation,
any merger or consolidation of the Corporation with or into any other
corporation, or any Asset Transfer, or any voluntary or involuntary dissolution,
liquidation or winding up of the Corporation, the Corporation shall mail to each
holder of Series A Preferred all notices, materials, proxy statements,
information statements and any other documents (including information that is
reasonably sufficient to enable such holders of Series A Preferred to make a
determination as to whether it would be to their advantage to convert their
shares of Series A Preferred to shares of Common Stock pursuant to this Section
4 prior to any transaction listed in (ii) above) distributed generally to the
holders of shares of Common Stock of the Corporation, at such times and by such
methods as such documents are distributed to such holders of Common Stock.

          m.   Automatic Conversion.

               (i)  Each share of Series A Preferred shall automatically be
converted into shares of Common Stock, based on the then-effective Conversion
Rate, on the tenth (10th) day after the day that the closing sale price (or the
closing bid, if no sales were reported) of the Common Stock on The Nasdaq
National Market has reached four (4) times the Closing Price (as adjusted for
any stock dividends, combinations, splits, recapitalizations and the like with
respect to the Common Stock) and remained at such level or higher for twenty
(20) consecutive trading days (the "TRIGGER PRICE LEVEL"); provided that such
Trigger Price Level shall have been reached after the earlier to occur of (A)
the unblinding and the public announcement of the results of the Corporation's
Phase II/III clinical trial of iseganan HCl for the prevention of
ventilator-associated pneumonia or (B) the second anniversary of the Original
Issue Date.

                                       8.
<PAGE>

               (ii) Upon a conversion in accordance with Section 4.m(i) above,
the outstanding shares of Series A Preferred shall be converted automatically
without any further action by the holders of such shares and whether or not the
certificates representing such shares are surrendered to the Corporation or its
transfer agent; provided, however, that the Corporation shall not be obligated
to issue certificates evidencing the shares of Common Stock issuable upon such
conversion unless the certificates evidencing such shares of Series A Preferred
are either delivered to the Corporation or its transfer agent as provided below,
or the holder notifies the Corporation or its transfer agent that such
certificates have been lost, stolen or destroyed and executes an agreement
satisfactory to the Corporation to indemnify the Corporation from any loss
incurred by it in connection with such certificates. Upon the occurrence of such
automatic conversion of the Series A Preferred, the holders of Series A
Preferred shall surrender the certificates representing such shares at the
office of the Corporation or any transfer agent for the Series A Preferred.
Thereupon, there shall be issued and delivered to such holder promptly at such
office and in its name as shown on such surrendered certificate or certificates,
a certificate or certificates for the number of shares of Common Stock into
which the shares of Series A Preferred surrendered were convertible on the date
on which such automatic conversion occurred. In lieu of delivering physical
certificates representing the Common Shares issuable upon conversion of Series A
Preferred, provided the Corporation's transfer agent is participating in the DTC
FAST program, upon request of the holder, and in accordance with applicable law,
the Corporation shall use its reasonable best efforts to cause its transfer
agent to electronically transmit the Common Shares issuable upon conversion to
the holder, by crediting the account of the holder's prime broker with DTC
through its DWAC system. The parties agree to coordinate with DTC to accomplish
this objective.

          n.   Fractional Shares. No fractional shares of Common Stock shall be
issued upon conversion of Series A Preferred. All shares of Common Stock
(including fractions thereof) issuable upon conversion of more than one share of
Series A Preferred by a holder thereof shall be aggregated for purposes of
determining whether the conversion would result in the issuance of any
fractional share. If, after the aforementioned aggregation, the conversion would
result in the issuance of any fractional share, the Corporation shall, in lieu
of issuing any fractional share, pay cash equal to the product of such fraction
multiplied by the Common Stock's fair market value (as determined in good faith
by the Board of Directors) on the date of conversion.

          o.   Reservation of Stock Issuable Upon Conversion. The Corporation
shall at all times reserve and keep available out of its authorized but unissued
shares of Common Stock, solely for the purpose of effecting the conversion of
the shares of the Series A Preferred, such number of its shares of Common Stock
as shall from time to time be sufficient to effect the conversion of all
outstanding shares of the Series A Preferred. If at any time the number of
authorized but unissued shares of Common Stock shall not be sufficient to effect
the conversion of all then outstanding shares of the Series A Preferred, the
Corporation will promptly take such corporate action as may, in the opinion of
its counsel, be necessary to increase its authorized but unissued shares of
Common Stock to such number of shares as shall be sufficient for such purpose.

          p.   Notices. All notices, requests, consents and other communications
hereunder shall be in writing, shall be mailed (A) if within domestic United
States by first-class

                                       9.
<PAGE>

registered or certified airmail, or nationally recognized overnight express
courier, postage prepaid, or by facsimile, or (B) if delivered from outside the
United States, by International Federal Express or facsimile, and shall be
deemed given (i) if delivered by first-class registered or certified mail
domestic, three (3) business days after so mailed, (ii) if delivered by
nationally recognized overnight carrier, one (1) business day after so mailed,
(iii) if delivered by International Federal Express, two (2) business days after
so mailed, (iv) if delivered by facsimile, upon electric confirmation of
receipt. All notices shall be addressed to each holder of record at the address
of such holder appearing on the books of the Corporation.

          q.   Payment of Taxes. The Corporation will pay all taxes (other than
taxes based upon income) and other governmental charges that may be imposed with
respect to the issue or delivery of shares of Common Stock upon conversion of
shares of Series A Preferred, excluding any tax or other charge imposed in
connection with any transfer involved in the issue and delivery of shares of
Common Stock in a name other than that in which the shares of Series A Preferred
so converted were registered.

     Section 5. Voting Rights.

          a.   General Rights. Except as otherwise provided herein or as
required by law, the Series A Preferred shall vote together with the Common
Stock at any annual or special meeting of the stockholders and not as a separate
class. Solely for the purposes of the voting rights pursuant to this Section 5,
each holder of shares of the Series A Preferred shall be entitled to the number
of votes equal to the number of shares of Common Stock into which such shares of
Series A Preferred could be converted based on a conversion price equal to the
closing bid price of the Common Stock on The Nasdaq National Market on the date
the Purchase Agreement is signed (as adjusted for stock splits, reverse stock
splits or other similar event affecting the Series A Preferred after the filing
date hereof) and shall have voting rights and powers equal to the voting rights
and powers of the Common Stock. Each holder of shares of Series A Preferred
shall be entitled to notice of any stockholders' meeting in accordance with the
bylaws of the Corporation.

          b.   Election of Directors. So long as at least 100 shares of Series A
Preferred (subject to adjustment for any stock split, reverse stock split or
other similar event affecting the Series A Preferred after the filing date
hereof) remain outstanding, (A) the holders of the Series A Preferred, voting
together as a separate class, shall be entitled to elect two (2) members of the
Board of Directors of the Corporation at each meeting of the Company's
stockholders for the election of directors, and to remove from office such
directors and to fill any vacancy caused by the resignation, death or removal of
such directors and (B) the holders of Common Stock and Series A Preferred,
voting together as a single class on an as-is-converted basis, shall be entitled
to elect the remaining members of the Board of Directors at each meeting of the
Company's stockholders for the election of directors, and to remove from office
such directors and to fill any vacancy caused by the resignation, death or
removal of such director.

     Notwithstanding anything set forth in this Section 5.b to the contrary, in
the event that the total number of shares of Series A Preferred (on an
as-is-converted basis) issued or issuable pursuant to the Purchase Agreement is
subject to the limitation of no greater than 19.9% of the Corporation's issued
and outstanding shares of Common Stock on the date of the Purchase

                                      10.
<PAGE>

Agreement (in accordance with the requirements of The Nasdaq Stock Market for
purposes of Rule 4350(i)(1)(D) thereof), then for so long as at least 100 shares
of Series A Preferred (subject to adjustment for any stock split, reverse stock
split or other similar event affecting the Series A Preferred after the filing
date hereof) remain outstanding, (A) the holders of the Series A Preferred,
voting together as a separate class, shall be entitled to elect one (1) member
of the Board of Directors of the Corporation at each meeting of the Company's
stockholders for the election of directors, and to remove from office such
director and to fill any vacancy caused by the resignation, death or removal of
such director and (B) the holders of Common Stock and Series A Preferred, voting
together as a single class on an as-is-converted basis, shall be entitled to
elect the remaining members of the Board of Directors at each meeting of the
Company's stockholders for the election of directors, and to remove from office
such directors and to fill any vacancy caused by the resignation, death or
removal of such directors.

          c.   Separate Vote of Series A Preferred. For so long as at least 100
shares of Series A Preferred (subject to adjustment for any stock split, reverse
stock split or other similar event affecting the Series A Preferred after the
filing date hereof) remain outstanding, in addition to any other vote or consent
required herein or by law, the vote of the holders of at least a majority of the
outstanding Series A Preferred shall be necessary for effecting or validating
the following actions:

               (i)  Any amendment, alteration, or repeal of any provision of the
Certificate of Incorporation (including any filing of a Certificate of
Designation), that alters or changes the voting or other powers, preferences, or
other special rights, privileges or restrictions of the Series A Preferred so as
to affect them adversely;

               (ii) Any authorization, designation or issuance, whether by
reclassification or otherwise, of any new class or series of stock or any other
securities convertible into equity securities of the Corporation ranking senior
to the Series A Preferred in right of liquidation preference, voting or
dividends; and

               (iii) Prior to the second (2nd) anniversary of the Original Issue
Date, any merger into or consolidation with any other corporation (other than a
wholly-owned subsidiary corporation or for the purposes of changing the domicile
of the Corporation) or the completion of any transaction or series of related
transactions in which fifty percent (50%) or more of the voting power of the
Corporation is transferred or any Asset Transfer.

     Section 6. No Reissuance of Series A Preferred . No shares of Series A
Preferred acquired by the Corporation by reason of redemption, purchase,
conversion or otherwise shall be reissued."

                                      11.
<PAGE>

     IN WITNESS WHEREOF, said INTRABIOTICS PHARMACEUTICALS, INC. has caused this
Certificate of Designation to be signed by its Chief Executive Officer as of May
1, 2003.

                                INTRABIOTICS PHARMACEUTICALS, INC.

                                By: /s/ Henry J. Fuchs
                                    -------------------------------
                                    Name: Henry J. Fuchs, M.D.
                                    Title: Chief Executive Officer

                                      12.