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                                                                     EXHIBIT 4.2

                               AMENDMENT NO. 1 TO
                           SECOND AMENDED AND RESTATED
                        PREFERRED SHARE RIGHTS AGREEMENT

     This Amendment No. 1 (this "Amendment") to Second Amended and Restated
Preferred Shares Rights Agreement (the "Rights Agreement") is made effective as
of April 26, 2001. This Amendment is an amendment to the Rights Agreement dated
August 21, 2000 between Cyberonics, Inc., a Delaware corporation (the
"Company"), and Fleet National Bank. (formerly known as BankBoston, N.A.,
formerly known as The First National Bank of Boston and referred to herein as
the "Rights Agent").

                                    RECITALS

     WHEREAS, pursuant to and in compliance with Section 27 of the Rights
Agreement, the Company and the Rights Agent wish to amend the Rights Agreement
as set forth herein;

     NOW THEREFORE, the parties hereto agree as follows:

     Section 1. Amendments. From and after the effective date of this Amendment,
the Rights Agreement shall be amended as follows:

     (a) The definition of "Acquiring Person" shall be amended to read in its
entirety as follows:

     "Acquiring Person" shall mean any person who or which, together with all
     Affiliates and Associates of such Person, shall be the Beneficial Owner of
     15% or more of the Common Shares then outstanding, but shall not include
     (i) the Company, (ii) any Subsidiary of the Company, (iii) any employee
     benefit plan of the Company or of any Subsidiary of the Company, or any
     entity holding Common Shares for, or pursuant to the terms of, any such
     plan, or (iv) any Exempt Person (so long as such Person remains an Exempt
     Person). Notwithstanding the foregoing, no Person shall be deemed to be an
     "Acquiring Person" as the result of an acquisition of Common Shares by the
     Company which, by reducing the number of shares outstanding, increases the
     proportionate number of shares beneficially owned by such Person to 15% or
     more of the Common Shares of the Company then outstanding; provided,
     however, that, if a Person shall become the Beneficial Owner of 15% or more
     of the Common Shares of the Company then outstanding by reason of share
     purchases by the Company and shall, after such share purchases by the
     Company, become the Beneficial Owner of any additional Common Shares of the
     Company (other than pursuant to a dividend or distribution paid or made by
     the Company on the outstanding Common Shares in Common Shares or pursuant
     to a split or subdivision of the outstanding Common Shares), then such
     Person shall be deemed to be an "Acquiring Person" unless upon becoming the
     Beneficial Owner of such additional Common Shares of the Company such
     Person does not beneficially own 15% or more of the Common Shares of the
     Company then outstanding.

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     Notwithstanding the foregoing, (i) if the Company's Board of Directors
     determines in good faith that a Person who would otherwise be an "Acquiring
     Person," as defined pursuant to the foregoing provisions of this paragraph
     (a), has become such inadvertently, and if such Person divested or divests
     as promptly as practicable a sufficient number or Common Shares so that
     such Person would no longer be an "Acquiring Person," as defined pursuant
     to the foregoing provisions of this paragraph (a), then such Person shall
     not be deemed to be or to have become an "Acquiring Person" for any
     purposes of this Rights Agreement, and (ii) if, as of the date hereof, any
     Person is the Beneficial Owner of 15% or more of the Common Shares
     outstanding, such Person shall not be or become an "Acquiring Person," as
     defined pursuant to the foregoing provisions of this paragraph (a), unless
     and until such time as Person shall become the Beneficial Owner of
     additional Common Shares (other than pursuant to a dividend or distribution
     paid or made by the Company on the outstanding Common Shares in Common
     Shares or pursuant to a split or subdivision of the outstanding Common
     Shares), unless, upon becoming the Beneficial Owner of such additional
     Common Shares, such Person is not then the Beneficial Owner of 15% or more
     of the Common Shares then outstanding.

     (d) Section 1 of the Rights Agreement shall be amended to add the
definition of "Exempt Person" as follows:

     "Exempt Person" shall mean the State of Wisconsin Investment Board
     ("SWIB"), unless such entity taken together with its Affiliates and
     Associates shall become the Beneficial Owner of 20% or more of the Common
     Shares outstanding subject to the same exceptions provided in the second
     and third sentences of the definition of "Acquiring Person" except that the
     reference to "15%" in such sentences shall be "20%" in the case of SWIB.

Section 27. Supplements and Amendments. Prior to the occurrence of a Triggering
Event, the Company may supplement or amend this Rights Agreement in any respect
without the approval of any holders of Rights, and the Rights Agent shall, if
the Company so directs, execute such supplement or amendment. From and after the
occurrence of a Triggering Event, the Company and the Rights Agent may from time
to time supplement or amend this Rights Agreement without the approval of any
holders of Rights in order to (i) cure any ambiguity, (ii) correct or supplement
any provision contained herein which may be defective or inconsistent with any
other provisions herein, (iii) shorten or lengthen any time period hereunder, or
(iv) to change or supplement the provisions hereunder in any manner that the
Company may deem necessary or desirable and that shall not adversely affect the
interests of the holders of Rights (other than an Acquiring Person or an
Affiliate or Associate of an Acquiring Person); provided, this Rights Agreement
may not be supplemented or amended to lengthen, pursuant to clause (iii) of this
sentence, (A) a time period relating to when the Rights may be redeemed at such
time as the Rights were not then redeemable or (B) any other time period unless
such lengthening is for the purpose of protecting, enhancing or clarifying the
rights of, and/or the benefits to, the holders of Rights (other than Acquiring
Person or an Affiliate or Associate of an Acquiring Person) and provided
further, that for so long as the State of Wisconsin Investment Board is an
"Exempt

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Person" (as defined herein), the definitions of "Exempt Person" and "Acquiring
Person" shall not be amended in any manner which would adversely affect the
application of such terms to the State of Wisconsin Investment Board without its
prior consent. Upon the delivery of a certificate from an appropriate officer of
the Company that states that the proposed supplement or amendment is in
compliance with the terms of this Section 27, the Rights Agent shall execute
such supplement or amendment. Prior to the Distribution Date, the interests of
the holders of Rights shall be deemed coincident with the interests of the
holders of Common Shares.

     (i) Exhibit B (Form of Rights Certificate) and Exhibit C (Summary of Rights
to Purchase Common Shares) to the Rights Agreement shall be amended to conform
to the changes in the Rights Agreement made and effected pursuant to this
Amendment.

     Section 2. Remainder of Agreement Not Affected. Except as set forth in
Section 1 hereof, the terms and provisions of the Rights Agreement shall remain
in full force and effect and are hereby ratified and confirmed.

     Section 3. Authority. Each party represents that such party has full power
and authority to enter into this Amendment, and that this Amendment constitutes
a legal, valid and binding obligation of such party, enforceable against such
party in accordance with its terms.

     Section 4. Definitions, References.

     (a) Unless otherwise specifically defined herein, each term used herein
which is defined in the Rights Agreement shall have the meaning assigned to such
term in the Rights Agreement.

     (b) On and after the effective date of this Amendment (i) all references in
the Rights Agreement, including Exhibits B and C, to the Rights Agreement shall
be deemed to refer to the Rights Agreement as amended by this Amendment, and all
prior amendments, and (ii) all references to "hereof," "hereunder," "herein,"
"hereby" and other similar references contained in the Rights Agreement as well
as each reference to "this Agreement" and each other similar reference contained
in the Rights Agreement shall refer to the Rights Agreement, as amended.

     Section 5. Counterparts. This Amendment may be executed in one or more
counterparts, each of which shall be deemed to be an original, but all of which
shall constitute one and the same agreement.

     IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed and attested, all as of the day and year first above written.

                                       CYBERONICS, INC.


                                       By: /s/ Robert P. Cummins
                                           -------------------------------------
                                           Robert P. Cummins
                                           Chief Executive Officer and President

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                                       FLEET NATIONAL BANK

                                       By: /s/ Joshua McGinn
                                           ----------------------
                                           Senior Account Manager

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