<PAGE>
 
                                                                   Exhibit 10.24

    SECOND AMENDMENT TO CONVERTIBLE SUBORDINATED DEBENTURE PURCHASE AGREEMENT

      THIS SECOND AMENDMENT TO CONVERTIBLE SUBORDINATED DEBENTURE PURCHASE
AGREEMENT (this "Second Amendment"), is made this 24 day of June, 1996, by and
between MEMRY CORPORATION, a Delaware corporation (the "Company"), and
CONNECTICUT INNOVATIONS, INCORPORATED, a specially chartered Connecticut
corporation ("CII"). All capitalized terms not otherwise defined herein shall
have the meanings ascribed to them in the Convertible Subordinated Debenture
Purchase Agreement dated December 22, 1994 between CII and the Company, as
amended by the First Amendment to Convertible Subordinated Debenture Purchase
Agreement dated October 12, 1995 (the "Agreement").

                             W I T N E S S E T H:

      WHEREAS, pursuant to the Agreement, the Company issued to CII a
convertible subordinated debenture, as amended (the "Debenture"), in the
original principal amount of $763,208 and certain warrants, as amended and
restated, of the Company described therein (the "Warrants"); and

      WHEREAS, the Company has executed that certain Asset Purchase Agreement by
and between the Company and Raychem Corporation, dated as of May 10, 1996 (as
amended from time to time, the "Asset Purchase Agreement"); and

      WHEREAS, as a condition to closing the Asset Purchase Agreement, the
Company must cause CII to convert the Debenture and waive certain defaults of
the Company under certain operative agreements between the Company and CII; and

      WHEREAS, the Company has requested and CII has agreed to convert the
Debenture and grant certain waivers upon the terms and conditions hereinafter
set forth.

      NOW, THEREFORE, in consideration of the promises and the mutual covenants
herein contained, the Company and CII agree as follows:
<PAGE>
 
                                  ARTICLE 1

                       CLOSING; CONDITIONS TO AMENDMENT

      Section 1.1 (a) The effectiveness of this Second Amendment shall occur at
a closing (the "Closing") at the offices of Shipman & Goodwin, One American Row,
Hartford, Connecticut on or before July 31, 1996 (the "Closing Date"), or at
such other place as may be agreed to by the parties hereto, simultaneously with
the closing of the transactions contemplated by the Asset Purchase Agreement.
All documents to be delivered at the Closing and acts to be performed thereat
shall be deemed to have taken place simultaneously.

      (b) At the Closing, CII shall deliver to the Company the Debenture, marked
"cancelled", in exchange for either (i) in the event that, by the date of the
Closing Date, the Company's Series G Preferred Stock, par value $100.00 per
share (the "Series G Preferred"), as a class, has been automatically converted
by its terms into Common Stock, 954,010 shares of Common Stock, or (ii) in the
event that, on the Closing Date, the Series G Preferred remains outstanding as a
class, both (x) 285,528 shares of Common Stock, and (y) 66.85 shares of a new
series of the Company's Series H Preferred Stock, par value $100.00 per share
(the "Series H Preferred"), having the rights, privileges and preferences set
forth in the form of Certificate of Designations, Preferences and Rights of
Series H Preferred Stock set forth as Exhibit A hereto (the "Series H
Certificate").

      Section 1.2 The Closing and the obligations of CII hereunder are subject
to the following conditions:

         (a) The Company shall close the Asset Purchase Agreement no later than
July 31, 1996 on the terms specified therein;

         (b) The representations and warranties made by the Company herein shall
be true and correct when made, and shall be true and correct in all respects at
the Closing Date as if made at and as of the Closing and with respect thereto,
after giving effect to the transactions contemplated hereby;

         (c) CII shall have received a Second Amendment to Escrow Agreement in
the form of Exhibit B hereto;

         (d) CII shall have received from the Company amended and restated Class
I Warrants in the form of Exhibit C hereto, amended and restated Class II
Warrants in the form of Exhibit D hereto and a Second Addendum to the Class III
Warrants in the form of Exhibit E hereto;

                                      - 2 -
<PAGE>
 
         (e) CII shall have received each of the other documents and items
listed below, all in form and substance satisfactory to CII:

               (i) Certificate of the Secretary of the Company, certifying: (i)
the accuracy of the corporate resolutions attached thereto authorizing the
transactions contemplated hereby and the execution of all necessary documents;
(ii) that the Certificate of Incorporation attached thereto has not been further
amended (other than the filing of the Series H Certificate) and is in full force
and effect; (iii) that the Bylaws attached thereto are accurate and have not
been further amended and are in full force and effect; and (iv) that the named
officers are incumbent and that their signatures are as shown;

               (ii) Certificates of Good Standing of recent date issued by the
Secretary of the State of Delaware and the Secretary of the State of Connecticut
for the Company;

               (iii) Tax clearance letters of recent date from the State of
Connecticut Department of Revenue Services for the Company (corporate business
tax and sales and use tax);

               (iv) Opinion letter of Company's counsel, Finn, Dixon & Herling
in form and substance satisfactory to CII; and

               (v) A closing check from the Company made payable to the order of
Shipman & Goodwin for its legal fees and expenses incurred in connection
herewith;

         (f) If any shares of the Series G Preferred remain outstanding on the
Closing Date, the board of directors of the Company shall have duly adopted and
the Company shall have duly filed with the Secretary of State of Delaware the
Series H Certificate, the Company shall have reserved for issuance a sufficient
number of shares of Series H Preferred Stock to allow for the conversion of the
Debenture as set forth herein, and the Company shall have reserved for issuance
a sufficient number of shares of Common Stock to allow for the conversion of
Series H Preferred Stock to be issued to CII pursuant to the terms of the Series
H Certificate;

         (g) If any shares of the Series G Preferred remain outstanding on the
Closing Date, the holders of shares representing at least two-thirds of the
voting power of the Series G Preferred shall have duly approved the issuance to
CII of a sufficient number of shares of the Series H Preferred to allow for the
conversion of the Debenture as set forth herein;

         (h) The Company shall have reserved for issuance a sufficient number of
shares of Common Stock to allow for the full exercise of the Warrants;

                                   - 3 -
<PAGE>
 
         (i) At least 29% of the outstanding shares of the Series G Preferred
shall have been or simultaneously shall be converted into Common Stock;

         (j) The Company shall be in full compliance with the terms, conditions
and covenants of the Debenture, including but not limited to, the timely payment
of interest, all of which accrued and unpaid interest must be paid prior to the
Closing;

         (k) The Company shall not have outstanding any preferred stock (except
for shares of Series G Preferred outstanding as of the Closing Date) or
convertible indebtedness (except for convertible indebtedness which is being
converted into Common Stock no later than the Closing Date) or other equity
securities which are senior to the Common Stock; and

         (l) All closing conditions shall be satisfied only upon the receipt by
CII's counsel of evidence reasonably satisfactory to CII's counsel that such
conditions have been satisfied.

                                  ARTICLE 2

                           AMENDMENTS TO AGREEMENT

      CII and the Company do hereby amend the Agreement as follows:

      Section 2.1 The term "Agreement" as used in the Agreement shall mean the
Agreement, as amended by this Second Amendment.

      Section 2.2 The terms "Class I Warrants," "Class II Warrants" and "Class
III Warrants" as used in the Agreement shall mean, respectively, the Class I
Warrants, as amended and restated pursuant to the terms hereof, the Class II
Warrants, as amended and restated pursuant to the terms hereof, and the Class
III Warrants, as amended by the Second Addendum thereto.

      Section 2.3 Section 2(a) shall be deleted in its entirety and replaced by
the following:

          (a) The Investor will not sell, assign, pledge, transfer, or otherwise
     dispose of, whether directly or indirectly, all or any portion of the
     Purchased Securities, or any Common Stock or any shares of the Company's
     Series H Preferred Stock, par value $100 per share (the "Series H Preferred
     Stock"), obtained upon the exercise or conversion of the Purchased
     Securities or upon the closing of the Second Amendment to this Agreement,
     or any Common Stock obtained upon conversion of the Series H Preferred
     Stock or any Common Stock obtained as a stock dividend on the Common Stock
     so obtained (such Common Stock and Series H Preferred Stock being
     hereinafter collectively referred to as the "Underlying Securities"; the
     Purchased Securities and the Underlying



                                     - 4 -
<PAGE>
 
     Securities are hereinafter collectively referred to as the "Securities")),
     to any person or entity without complying with applicable securities laws;

      Section 2.4 Section 4.1(b) shall be deleted in its entirety and replaced
by the following:

          (b) The term "Registrable Securities" means any Common Stock obtained
     by the Investor upon exercise or conversion of the Purchased Securities or
     upon the closing of the Second Amendment to this Agreement, upon conversion
     of the Series H Preferred Stock or as a stock dividend on the Common Stock
     so obtained owned or acquirable upon the exercise of the Class III Warrants
     (as described below), excluding, however, any Registrable Securities (x)
     sold by a person in a transaction in which its rights under this Section 4
     are not assigned, (y) sold pursuant to a registration statement declared
     effective by the Securities and Exchange Commission, and (z) saleable under
     paragraph (k) of Rule 144.

      Section 2.5 Section 4.1(d) shall be deleted in its entirety and replaced
by the following:

          (d) The terms "Form S-2" and "Form S-3" means such forms under the Act
     as in effect on the date hereof or any registration form under the Act
     subsequently adopted by the Securities and Exchange Commission (the "SEC")
     which permits including or incorporation of substantial information by
     reference to other documents filed by the Company with the SEC.

      Section 2.6 Sections 4.2(a)(i) and 4.2(a)(ii) shall be deleted in their
entirety and replaced by the following:

          (i) no later than October 31, 1996, file a registration statement (the
     "Registration Statement") covering inter alia, the resale by the Investor
     of the Registrable Securities acquired by it pursuant to this Agreement,
     which registration statement may cover the concurrent registration of the
     resale of (A) the shares of Common Stock issued by the Company to certain
     individuals and entities prior to October 12, 1995 and to be issued by the
     Company as set forth on Schedule A hereto, which shares of Common Stock the
     Company may be required to register pursuant to the terms of existing
     agreements in effect on the date of closing of the Second Amendment to this
     Agreement, (B) the shares of Common Stock underlying the Company's Series G
     Preferred Stock issued by the Company pursuant to those certain Securities
     Purchase Agreements dated as of June 14, 1995, and (C) the shares of Common
     Stock issued, or issuable upon the conversion of convertible securities
     issued, in connection with the transactions contemplated by the Asset
     Purchase Agreement, as described on Schedule A hereto, or as otherwise
     described on Schedule A hereto; provided,



                                     - 5 -
<PAGE>
 
     however, that if the registration is underwritten and a limitation on the
     aggregate number of shares being sold thereby is required, the Registrable
     Securities shall have priority over all of the securities held by
     stockholders of the Company other than Raychem Corporation, and shall have
     the right to participate pari passu with Raychem Corporation based upon
     their respective stockholdings (on a fully diluted basis), (ii) cause such
     Registration Statement to become effective no later than January 31, 1997,

      Section 2.7 The first paragraph of Section 4.9 and Section 4.9(d) are
hereby amended by inserting the phrase "Form S-2 or" prior to "Form S-3."

      Section 2.8 Section 4.9(b) is hereby amended by inserting the phrase "At
such time as the Common Stock is listed and registered on a national securities
exchange or is quoted on the automated quotation system of a national securities
association," at the beginning of such section.

      Section 2.9 The last sentence of Section 6.5 shall be deleted and replaced
by the following:

     In the event the Investor exercises its rights pursuant to this Section
     6.5, the phrase "and Class III Warrants" shall be deemed to be inserted
     after the phrase "Class II Warrants" in clauses (i)(c) and (iii)(y) of the
     definition of Put Price in Section 8 hereof after the phrase "Class II
     Warrants."

      Section 2.10 The definition of "Connecticut Presence" in Section 8 shall
be deleted in its entirety and replaced by the following:

          Connecticut Presence - shall mean (i) maintaining its corporate
     headquarters and all of its product business operations in the State of
     Connecticut, including, but not limited to, after January 1, 1997, the
     assembly of all products to be sold to the U.S. Surgical Corporation, but
     excluding its business operations related to Wright Machine Corporation's
     business related to the production of screw machine products and taper pins
     and the Company's components and sub-assembly business to be acquired from
     Raychem Corporation to be carried out in the State of California, (ii)
     basing its president and chief executive officer, a majority of its senior
     executives, and all of its administrative, financial, research and
     development, marketing and customer service staff related to its product
     business, including, but not limited to, after January 1, 1997, the
     assembly of all products to be sold to the U.S. Surgical Corporation, (but
     excluding Wright Machine Corporation's business related to the production
     of screw machine products and taper pins and the Company's components and
     sub-assembly business to be acquired from Raychem 



                                     - 6 -
<PAGE>
 
     Corporation to be carried out in the State of California) in the State of
     Connecticut, (iii) conducting all of its operations (including
     manufacturing and production) related to its product business, directly or
     through subcontractors and through licensed operations, in the State of
     Connecticut, including, but not limited to, after January 1, 1997, the
     assembly of all products to be sold to the U.S. Surgical Corporation, but
     excluding Wright Machine Corporation's business related to the production
     of screw machine products and taper pins and the Company's components and
     sub-assembly business to be acquired from Raychem Corporation to be carried
     out in the State of California, and (iv) maintaining its principal bank
     accounts with banks located in the State of Connecticut, excluding all
     banks associated with Wright Machine Corporation. Each failure to comply
     with any of the clauses set forth in this definition shall constitute a
     failure to maintain a "Connecticut Presence."

      Section 2.11 The definition of "Put Price" in Section 8 shall be deleted
in its entirety and replaced by the following:

          Put Price - shall mean the sum of the following:

          (i) the product of the Multipler multiplied by the number of shares of
     Common Stock held by the Investor on the date of the Put Closing which were
     obtained by the Investor (a) upon the closing of the Second Amendment to
     this Agreement, (b) upon conversion of shares of Series H Preferred Stock
     obtained upon the closing of the Second Amendment to this Agreement, (c)
     upon exercise of any or all of the Class I Warrants and Class II Warrants,
     and (d) pursuant to a stock dividend or stock split with respect to the
     shares of Common Stock referred to in clauses (a) through (c) above;

          (ii) the product of the Multiplier multiplied by the number of shares
     of Common Stock acquirable upon the conversion of shares of Series H
     Preferred Stock held by the Investor on the date of the Put Closing which
     shares of Series H Preferred Stock were obtained upon the closing of the
     Second Amendment to this Agreement; and

          (iii) the difference between (x) the Multiplier multiplied by the
     number of shares of Common Stock acquirable upon the exercise of the
     remaining Class I Warrants and Class II Warrants, minus (y) any exercise
     prices that would have to be paid upon full exercise of the remaining Class
     I Warrants and Class II Warrants.

      Section 2.12 The definition of Registration Default in Section 8 shall be
deleted in its entirety and replaced by the following:


                                     - 7 -
<PAGE>
 
          Registration Default - Either (i) the breach by the Company of the
     provisions of Section 4.2(a) (i) and/or (ii) above, or (ii) the failure by
     the Company to keep the Registration Statement effective, free from any
     stop orders issued by the SEC or suspensions by the Company pursuant to
     Section 4.4(b) above (other than suspensions the notice of which is
     accompanied by a certificate signed by the President and at least 80% of
     the members of the Board of Directors of the Company and prepared in good
     faith stating that, in the good faith judgment of the Board of Directors of
     the Company it would be seriously detrimental to the Company for the
     Investor to effect sales of Registerable Securities included in a
     registration statement at such time and the reason therefor (it being
     understood by the Investor that such reason may be material, non-public
     information)), for an aggregate of 120 days during any rolling twelve month
     period (it being agreed and understood that, upon the occurrence of a
     Registration Default pursuant to this clause (ii), no new rolling twelve
     month period pursuant to this clause (ii) shall commence prior to the date
     of such Registration Default).

      Section 2.13 The reference to "October 12, 1995" in the definition of
Expiration Date in Section 8 shall be deleted and replaced by "Subsequent
Closing Date (as hereinafter defined)."

      Section 2.14 The following shall be added to the end of Section 8:

          Subsequent Closing Date - shall mean the date upon which the Closing
     of that certain Second Amendment, dated June 24, 1996, to this Agreement
     occurs.

          Multiplier - shall mean the greater of (i) the Current Market Price on
     the Put Date, or (ii) $2.00 (subject to adjustments for subdivisions, stock
     dividends, stock splits or consolidations of Common Stock).

                                  ARTICLE 3

                  REPRESENTATIONS, WARRANTIES AND COVENANTS
                                OF THE COMPANY

      Section 3.1 All action on the part of the Company, its directors and
stockholders necessary for the authorization, execution, delivery and
performance by the Company of this Agreement and the consummation of the
transactions contemplated herein, and for the authorization, execution and
delivery of the Warrants and, if applicable, the Series H Preferred have been
taken or will be taken prior to the Closing. This Second Amendment, and the


                                     - 8 -
<PAGE>
 
Agreement as amended hereby, is a valid and binding obligation of the Company,
enforceable in accordance with its terms against the Company.

      Section 3.2 The Company hereby makes to CII all of the representations and
warranties that it is making to Raychem Corporation pursuant to the Asset
Purchase Agreement to the same extent as if such representations and warranties
were set forth in full herein.

      Section 3.3 Neither this Agreement as amended hereby, nor any other
written statement furnished to CII nor its counsel in connection with the
transaction contemplated hereby contains any untrue statement of a material fact
or omits to state a material fact necessary in order to make the statements
contained therein or herein not misleading in the light of the circumstances
under which they were made.

      Section 3.4 Each of the key employees and consultants of the Company and
of each subsidiary listed on Schedule B hereto, other than persons to become key
employees of the Company in connection with the closing of the Asset Purchase
Agreement (the "Raychem Employees"), has entered into a confidentiality
agreement, a non-competition agreement, a proprietary information and invention
agreement and/or an employment agreement, true and accurate copies of which have
been provided to CII. The Company hereby covenants and agrees to use its best
efforts to cause each of the Raychem Employees to enter into a confidentiality
agreement, a proprietary information and inventions agreement and/or employment
agreement no later than July 15, 1996.

      Section 3.5 There are no "side agreements" or other agreements or
understandings between the Company and any third party providing compensation or
other consideration to any third party in connection with the conversion of
Series G Preferred into Common Stock, except for the terms of the Certificate of
Designations, Rights and Preferences of said Series G Preferred Stock.

      Section 3.6 The Company represents and warrants that it has fully complied
with each of the covenants contained in Section 5 of the Agreement and there
exists no default or Event of Default under the Agreement or Debenture and no
event has occurred which with the passage of time would constitute an Event of
Default, other than the Company's failure to file and effect a registration of
the Registrable Securities by March 15, 1996.

      Section 3.7 The Company represents and warrants that except as set forth
on Part I of Schedule C hereto, and with respect to the registration rights
granted to CII, there are no "side agreements" or other agreements or
understandings with any person regarding registration of securities of the
Company under the Securities Act of 1933, as amended. Except as set forth on
Part II of Schedule C hereto, between July 1, 1995 and the date hereof, no
securities of the Company have been sold which provide registration or other
rights more favorable than those set forth herein. In the event that the Company
grants registration rights to any other holder 



                                     - 9 -
<PAGE>
 
of securities of the Company, the Company will promptly give to CII written
notice thereof and, if in the opinion of CII such registration rights are more
favorable than the registration rights provided under this Agreement, CII shall
so notify the Company within thirty (30) days of receipt of the foregoing notice
from the Company, whereupon such registration rights shall automatically be
deemed to be incorporated in this Agreement in substitution of the registration
rights currently granted by this Agreement.

      Section 3.8 The Company represents and warrants that during the six-month
period ending on the Closing Date the Company has not issued, and does not
currently intend to issue, any capital stock of any class which has rights to be
preferred as to dividends or as to the distribution of assets upon voluntary or
involuntary liquidation, dissolution or winding up ("Preferred Securities"),
other than the shares of Series H Preferred which may be issued to CII upon
conversion of the Debenture.

      Section 3.9 The Company represents and warrants that except as set forth
on Part II of Schedule C hereto, during the six-month period ending and
including the Closing Date, the Company has not issued, and does not currently
intend to issue any "Additional Common Shares" (as such term is defined in the
Debenture) for a consideration per share less than $0.80.

                                  ARTICLE 4

               REPRESENTATIONS, WARRANTIES AND COVENANTS OF CII

      Section 4.1 CII hereby restates each of the representations and warranties
of CII contained in Section 2 of the Agreement, as amended hereby (other than
Section 2(j) thereof), and represents and warrants that each such representation
and warranty is true and correct on the date hereof and will be true and correct
on the date of the Closing.

      Section 4.2 Effective upon the Closing, CII hereby waives its rights and
remedies pursuant to the Agreement and the Debenture with respect to the
Company's failure to file and effect a registration of Registrable Securities by
March 15, 1996 (including without limitation its right to receive any adjustment
to the Common Stock Conversion Price (as defined in the Debenture) pursuant to
Section 2.3 of the Debenture), provided that such waiver shall not extend to or
affect the right of CII to receive additional interest pursuant to the second
paragraph of the Debenture or any subsequent default under the Agreement, as
amended hereby, or impair any right consequent thereon.


                                     - 10 -
<PAGE>
 
                                  ARTICLE 5

                                MISCELLANEOUS

      Section 5.1 The Company will pay all expenses in connection with the
subject matter of this Second Amendment, including the fees and disbursements of
CII's special counsel.

      Section 5.2 Except as expressly modified herein, all other terms,
conditions and obligations of the Agreement are hereby ratified and confirmed.

      Section 5.3 This Agreement may be executed in two or more counterparts,
each of which shall be deemed an original but all of which together will
constitute one and the same instrument.

                 [The following page is the signature page.]


                                     - 11 -
<PAGE>
 
      IN WITNESS WHEREOF, this Second Amendment has been duly signed, sealed and
delivered by the Company and CII as of the date and year first above written.

                                CONNECTICUT INNOVATIONS, INCORPORATED

                                By: /s/ Victor R. Budnick
                                   --------------------------------------------
                                   Its: President and Executive Director
                                   Duly Authorized

                                MEMRY CORPORATION

                                By: /s/ James G. Binch
                                   --------------------------------------------
                                   Its: President
                                   Duly Authorized

                                     - 12 -
<PAGE>
 
                  EXHIBITS AND SCHEDULES INTENTIONALLY OMITTED











                                     - 13 -