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                                                                    EXHIBIT 10.4

                               EPIX MEDICAL, INC.

                              STANDSTILL AGREEMENT

         THIS AGREEMENT, dated as of June 9, 2000, is between SCHERING BERLIN
VENTURE CORPORATION, a Delaware corporation having a place of business at 340
Changebridge Road, Montville, New Jersey (the "Purchaser"), and EPIX MEDICAL,
INC. (the "Company"), a Delaware corporation having a place of business at 71
Rogers Street, Cambridge, Massachusetts 02142.

                                   WITNESSETH:

         WHEREAS on the date hereof, the Purchaser has agreed to acquire
1,112,075 shares (the "Shares") of common stock, $.01 par value per share
("Common Stock"), of the Company pursuant to the terms of a Stock Purchase
Agreement dated as of the date hereof (the "Stock Purchase Agreement"); and

         WHEREAS the execution and delivery of this Agreement by the Purchaser
is a condition precedent to the Company's obligations under the Stock Purchase
Agreement and a Strategic Collaboration Agreement (the "Collaboration
Agreement") among the parties dated as of the date hereof;

         NOW, THEREFORE, in consideration of the premises and of the mutual
covenants and agreements set forth herein and for other good and valuable
consideration the receipt of which is hereby acknowledged, the parties,
intending to be legally bound hereby, agree as follows:


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                                    ARTICLE I

                         REPRESENTATIONS AND WARRANTIES

         The Purchaser hereby represents and warrants to the Company as follows:

                  (a) The Purchaser has all requisite corporate power and
authority to enter into and perform this Agreement. The execution and delivery
of this Agreement by the Purchaser and the consummation by it of the
transactions contemplated hereby have been duly authorized by all necessary
corporate action on behalf of the Purchaser. This Agreement is a valid and
binding obligation of the Purchaser enforceable against it in accordance with
its terms, except that such enforcement may be subject to (i) bankruptcy,
fraudulent conveyance, insolvency, reorganization, moratorium or other similar
laws now or hereafter in effect relating to creditors' rights and contracting
parties' rights generally and (ii) general principles of equity (regardless of
whether such enforcement is considered in a proceeding in equity or at law).

                  (b) Neither the execution and delivery of this Agreement by
the Purchaser nor the consummation by it of the transactions contemplated hereby
conflicts with or constitutes a violation of or default under the charter,
by-laws or other organizational document of the Purchaser, any statute, law,
regulation, order or decree applicable to the Purchaser, or any material
contract, commitment, agreement, arrangement or restriction of any kind to which
the Purchaser is a party or by which it is bound.

                                   ARTICLE II

                          LIMITATIONS AND RESTRICTIONS

         Section 2.01      DEFINITIONS.  As used in this Agreement:

                  (a) "Affiliate" shall mean any entity controlling, controlled
by or under common control with the Purchaser, and "control" shall mean
ownership of more than 50% of stock entitled to vote for directors or more than
50% of the equity of any non-corporate entity;

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                  (b) "group" shall have the meaning with which such term is
used in Section 13(d)(3) of the Securities Exchange Act of 1934, as amended (the
"Exchange Act"); and

                  (c) "person" shall have the meaning with which such term is
used in Section 2(2) of the Securities Act of 1933, as amended (the "Securities
Act").

         Section 2.02 RESTRICTIONS ON CERTAIN ACTIONS BY THE PURCHASER. Except
(i) with the written consent of the Company, (ii) by way of stock dividends or
other distributions or offerings made available to the Company's shareholders
generally, or (iii) pursuant to a merger, reclassification, recapitalization or
other similar transaction approved by the Company's Board of Directors, the
Purchaser agrees that during the term of this Agreement, it will not, and it
will use reasonable efforts to cause its Affiliates not to:

                  (a) for a period of one year following the date hereof, sell,
exchange, transfer or otherwise dispose of the Shares;

                  (b) acquire, announce an intention to acquire, offer or
publicly propose to acquire, solicit an offer to sell or agree to acquire, by
purchase, by gift, by joining a partnership, limited partnership, syndicate or
other group or otherwise, any shares of Common Stock or other voting securities
of the Company, or any other Company securities convertible into, exchangeable
for or exercisable for Common Stock or other voting securities of the Company
(all such securities, collectively, "Voting Securities"); provided, however,
that this Section 2.02(b) shall not apply unless and until (and then only so
long as) the Purchaser (together with its Affiliates) has beneficial ownership
(as such term is used under Section 13(d) of the Exchange Act) of five percent
(5%) or more of the outstanding Common Stock determined on a fully diluted
basis;

                  (c) participate in the formation of any group, or join with
any group, which owns or seeks to acquire beneficial ownership of Voting
Securities, for the purpose of acquiring Voting Securities;

                  (d) solicit, or participate in any "solicitation" of "proxies"
or become a "participant" in any "election contest" (as such terms are defined
or used in Regulation 14A under

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the Exchange Act, these terms to have such meaning throughout this Agreement)
with respect to the Company;

                  (e) initiate, publicly propose or otherwise solicit
stockholders for the approval of, one or more stockholder proposals with respect
to the Company, or induce any other person to initiate any stockholder proposal;

                  (f) seek to place any representative on the Board of Directors
of the Company, or seek to have called any meeting of the stockholders of the
Company;

                  (g) deposit any Voting Securities in a voting trust or subject
them to a voting agreement or other agreement or arrangement with respect to the
voting of such Voting Securities, other than this Agreement;

                  (h) otherwise act, alone or in concert with others, to seek to
control the management, Board of Directors, policies or affairs of the Company
or solicit, publicly propose, seek to effect or negotiate with any other person
with respect to any form of business combination or other extraordinary
transaction with the Company or any restructuring, recapitalization or similar
transaction with respect to the Company, or solicit, make or publicly propose or
negotiate with any other person with respect to, or announce an intent to make,
any tender offer or exchange offer for any securities of the Company, or
publicly disclose an intent, purpose, plan or proposal with respect to the
Company, or any securities or assets of the Company, that would violate the
provisions of this Section 2.02, or assist, participate in, facilitate or
solicit any effort or attempt by any person to do so or seek to do any of the
foregoing.

         Section 2.03 EMPLOYEE BENEFIT PLANS. For the avoidance of doubt, it is
hereby agreed that the restrictions contained in Section 2.02 shall not apply to
any pension plan or other employee benefit plan of the Purchaser or its
Affiliates which is administered by an independent trustee or trustees.

         Section 2.04 FREEDOM TO VOTE. Nothing contained herein shall prevent
the Purchaser or any of its Affiliates from voting any equity securities owned
by them in their sole discretion, and to

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that extent, seeking to influence the policies or affairs of the Company or to
approve or disapprove of any matter put to a vote of the stockholders of the
Company.

                                   ARTICLE III

                                  MISCELLANEOUS

         Section 3.01 INTERPRETATION. For all purposes of this Agreement, the
term Common Stock shall include any securities of the Company entitled to vote
generally for the election of directors of the Company which securities the
holders of the Common Stock shall have received or as a matter of right be
entitled to receive as a result of (i) any capital reorganization or
reclassification of the capital stock of the Company or (ii) any consolidation,
merger or share exchange of the Company with another corporation in which the
Company survives after such transaction; provided, however, that nothing in this
Agreement shall preclude the Purchaser or its Affiliates from acquiring or being
entitled to acquire Common Stock in exchange for their shares of stock in the
Company in any such transaction.

         Section 3.02 ENFORCEMENT. (a) The Purchaser acknowledges and agrees
that irreparable damage would occur if any of the provisions of this Agreement
were not performed in accordance with their specific terms or were otherwise
breached and that monetary damages would be an inadequate remedy therefor.
Accordingly, the Company will be entitled to seek an injunction or injunctions
to prevent breaches of this Agreement and to enforce specifically its provisions
in any court of the United States or any state having jurisdiction, this being
in addition to any other remedy to which the Company may be entitled at law or
in equity.

                  (b) No failure or delay on the part of the Company in the
exercise of any power, right or privilege hereunder shall operate as a waiver
thereof, nor shall any single or partial exercise of any such power, right or
privilege preclude other or further exercise thereof or of any other right,
power or privilege.

         Section 3.03 ENTIRE AGREEMENT. This Agreement, the Stock Purchase
Agreement and the Collaboration Agreement constitute the entire understanding of
the parties with respect to the

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transactions contemplated hereby. This Agreement may be amended only by an
agreement in writing executed by all the parties hereto.

         Section 3.04 SEVERABILITY. If any provision of this Agreement is held
by a court of competent jurisdiction to be unenforceable, the remaining
provisions shall remain in full force and effect. It is declared to be the
intention of the parties that they would have executed the remaining provisions
without including any that may be declared unenforceable.

         Section 3.05 HEADINGS. Descriptive headings are for convenience only
and will not control or affect the meaning or construction of any provision of
this Agreement.

         Section 3.06 COUNTERPARTS. This Agreement may be executed in one or
more counterparts, and each such executed counterpart will be an original
instrument.

         Section 3.07 NOTICES. All notices, consents, requests, instructions,
approvals and other communications provided for in this Agreement will be
validly given or made, if in writing and delivered personally or sent by
registered mail postage paid:

if to the Company:                  EPIX Medical, Inc.
                                    71 Rogers Street
                                    Cambridge, MA 02142
                                    Attention:  Chief Executive Officer
                                    Tel: (617) 250-6000
                                    Fax: (617) 250-6031

with a copy to:                     William T. Whelan, Esq.
                                    Mintz, Levin, Cohn, Ferris,
                                    Glovsky and Popeo, P.C.
                                    One Financial Center
                                    Boston, MA  02111
                                    Tel: (617) 542-6000
                                    Fax: (617) 542-2241

if to the Purchaser:                Schering Berlin Venture Corporation
                                    340 Changebridge Road
                                    Montville, NJ 07045-1000
                                    Attention: Treasurer
                                    Tel: (973) 276-2000
                                    Fax: (973) 276-2005


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or to such other address or telecopy number as any party may, from time to time,
designate in a written notice given in a like manner. Notice by telecopy shall
be deemed delivered on the day telephone confirmation of receipt is given.

         Section 3.08 SUCCESSORS AND ASSIGNS. This Agreement shall bind the
successors and assigns of the parties, and inure to the benefit of any successor
or assign of any of the parties; provided, however, that no party may assign
this Agreement without the other party's prior written consent, and provided,
further, that this Agreement shall not be binding upon any purchaser of the
Shares from the Purchaser or an Affiliate of the Purchaser in a transaction
effected on a public trading market or pursuant to a public offering.

         Section 3.09 TERM. The term of this Agreement shall commence on the
date first referred to above and terminate upon the earliest to occur of (i) the
termination of the Collaboration Agreement, (ii) the Board of Directors of the
Company approving any proposal or offer involving (v) a merger, consolidation,
dissolution, recapitalization or other business combination involving the
Company and in which the Company does not survive, including a sale of all or
substantially all of the assets of the Company, (w) the issuance by the Company
of a majority of its outstanding equity securities (on a fully diluted basis) in
consideration for the assets or securities of another person, (x) the
acquisition by any person or group of beneficial ownership in any manner of a
majority of the Company's outstanding equity securities (on a fully diluted
basis), or (y) the acquisition by any entity (or group that includes any entity)
engaged in the business of selling or marketing diagnostic imaging agents (a
"competitor") of more than 35% of the Company's outstanding equity securities
(on a fully diluted basis), provided that such competitor itself acquires more
than 20% of such equity securities, or (z) the election to the Board of
Directors of the Company of any person designated by a competitor, (iii) the
public announcement of an intent to commence or the commencement by any person
or group other than the Purchaser or any Affiliate of the Purchaser of a tender
offer or an exchange offer for the securities of the Company, and (iv) the third
anniversary of the date hereof.


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         Section 3.10 GOVERNING LAW. This Agreement shall be governed by and
construed and enforced in accordance with the laws of the State of Delaware,
without giving effect to the conflict of laws principles thereof.

         IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
executed as of the date first referred to above.

                                        EPIX MEDICAL, INC.

                                        By:      /s/ MICHAEL D. WEBB
                                           ---------------------------------
                                                 Michael D. Webb
                                                 Chief Executive Officer

                                        SCHERING BERLIN VENTURE CORPORATION

                                        By:      /s/ JOHN NICHOLSON
                                           ---------------------------------
                                                 John Nicholson
                                                 Treasurer


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