EXHIBIT 3.4

                                    AGREEMENT

      THIS AGREEMENT (the "AGREEMENT") is made and entered into as of this 17th
day of February, 2004 by and among (a) Arwol Holdings Ltd. ("ARWOL") (b) Macpell
Industries Ltd. ("MACPELL" and, collectively with Arwol, the "SELLERS"), and (c)
Norfet, Limited Partnership (the "PURCHASER"), a limited partnership registered
under the laws of the State of Israel.

      WHEREAS, the Purchaser is an Israeli limited partnership wholly owned by
(x) N.D.M.S Ltd. ("NDMS"), an Israeli private company, controlled by FIMI
Opportunity Fund, L.P. (the "DELAWARE FUND"), a limited partnership formed under
the laws of the State of Delaware, (y) FIMI Israel Opportunity Fund, Limited
Partnership (the "ISRAELI FUND"), a limited partnership, formed under the laws
of the State of Israel, and (z) certain designees and co-investors listed in
EXHIBIT A attached hereto (collectively with the Delaware Fund and the Israeli
Fund, the "FUND");

      WHEREAS, Arwol is a private Israeli company wholly owned by Arie Wolfson;

      WHEREAS, Macpell is an Israeli public company whose shares are traded on
the Tel Aviv Stock Exchange;

      WHEREAS, Tefron Ltd. (the "COMPANY"), is an Israeli public company whose
shares are traded on the New York Stock Exchange (the "NYSE");

      WHEREAS, the Purchaser had offered Arwol to purchase 1,365,000 Series A
Ordinary Shares of the Company, nominal value NIS 1.00 each (the "PURCHASED
SHARES") and, as a material condition for such purchase at the price and under
the terms provided herein, had desired to establish certain terms regarding
their cooperation as controlling shareholders of the Company as set forth
herein;

      WHEREAS, at the request of Arwol, the Purchaser agreed to Arwol's offering
Macpell to participate in such sale and to sell up to 50% of the Purchased
Shares;

      WHEREAS, Macpell has decided to sell 50% of the Purchased Shares, such
that each of Macpell and Arwol shall sell to the Purchaser 682,500 Series A
Ordinary Shares of the Company, together constituting the entire amount of the
Purchased Shares;

      WHEREAS, on even date hereof, the Purchaser is entering into a Share
Purchase Agreement (the "TEFRON PURCHASE AGREEMENT") with the Company, pursuant
to which it will purchase 3,529,412 Series A Ordinary Shares of the Company.
Immediately following the consummation of the purchase transactions contemplated
herein and in the Tefron Purchase Agreement, the Purchaser will hold 4,894,412
Series A Ordinary Shares of the Company, representing approximately 30.7% of the
Company's issued share capital (excluding shares held by the Company's
subsidiary) and Arwol and Macpell will, collectively, hold at least 4,842,325
Series A Ordinary Shares of the Company representing approximately 30.37% of the
Company's issued share capital (excluding shares held by the Company's
subsidiary); and


<PAGE>


      WHEREAS, the parties wish to set forth the terms and conditions of the
sale of the Purchased Shares to the Purchaser and the terms and conditions
applicable to the parties' relationship as of the Closing (as defined below),
all according to the terms and conditions herein contained.

      NOW, THEREFORE, in consideration of the mutual promises contained in this
Agreement and other good and valuable consideration, the receipt and sufficiency
of which is hereby acknowledged, the parties hereto agree as follows:

                                    ARTICLE I
                               PURCHASE OF SHARES;
                             PURCHASE PRICE; CLOSING

1.1 PURCHASE OF SHARES.

Subject to the terms and conditions hereof and in reliance upon the
representations, warranties and agreements contained herein, at the Closing,
each of the Sellers shall sell to the Purchaser, and the Purchaser shall
purchase from each of the Sellers 682,500 Series A Ordinary Shares of the
Company (together constituting the entire number of Purchased Shares), free from
all Encumbrances (as defined below), for a price per share equal to US$ 5.538
for each of the Purchased Shares (the "PRICE PER SHARE"), which amounts to an
aggregate purchase price equal to US$ 7,559,370 (the "PURCHASE PRICE").

Notwithstanding anything to the contrary herein, upon their mutual written
notice to the Purchaser (to be delivered by no later than three (3) business
days before the Closing) Macpell and Arwol shall be entitled to change the
amount of shares to be sold by each of them, without the need to receive the
Purchaser's approval, provided however, that in any event the aggregate amount
of the Purchased Shares to be sold by both Sellers shall be 1,365,000 and shall
not affect their respective undertakings pursuant to Article V below.

For the purpose of avoiding any doubt, it is hereby clarified that the
representations and undertakings taken by Macpell and Arwol herein are given
severally, and none of Sellers shall bear any responsibility for the other's
act, omission or breach of this Agreement; however, none of the sale
transactions contemplated herein shall be effectuated unless the other is
simultaneously effectuated as well, in a manner that the Purchaser shall
purchase the entire amount, and not less than the entire amount, of the
Purchased Shares.


                                       2
<PAGE>


(b) PRICE PER SHARE ADJUSTMENTS

Notwithstanding the foregoing, in the event that the Company's earnings before
income tax, depreciation and amortization (the "EBITDA") (excluding (i) the
EBITDA of Alba Health LLC ("ALBAHEALTH") to the extent it exceeds zero and (ii)
any increase in the EBITDA of Alba Waldensian, Inc. ("ALBA") as a result of the
exercise of the Put Option (as such term is defined in the Tefron Purchase
Agreement) for fiscal year 2004 (the "2004 EBITDA"), as set forth in the
Company's audited consolidated financial statements for the year ending on
December 31, 2004 (the "2004 FINANCIALS"), is less than US$23 million, then the
Price Per Share shall be adjusted as follows: (i) if the Company's EBITDA is
equal to or lower than US$16 million, then the Price Per Share will be
retroactively reduced by US$0.75 (i.e., to US$4.788), and (ii) if the Company's
EBITDA is higher than US$16 million but lower than US$23 million, the Price Per
Share will be retroactively reduced, as follows:

PPS= 5.538 - 0.75*[X]

X=[(23,000,000 -2004 EBITDA)/1,000,000]/7]

The Price Per Share, as reduced, shall be referred to herein as the "ADJUSTED
PPS".

In the event that the Adjusted PPS is not equal to the Price Per Share, each
Seller, at its sole discretion, shall either (i) deliver to the Purchaser,
within fourteen (14) business days following the release of the 2004 Financials,
a number of additional Ordinary Shares (the "ADDITIONAL SHARES") that is equal
to the difference between the number of Purchased Shares sold to the Purchaser
by such Seller at the Closing and the number of Ordinary Shares that would have
been delivered to the Purchaser by such Seller at the Closing had the original
Price Per Share been equal to the Adjusted PPS, or (ii) pay the Purchaser,
within ten (10) business days following the release of the 2004 Financials, a
cash amount equal the difference between the Price Per Share and the Adjusted
PPS per each share purchased by the Purchaser from such Seller hereunder.

     (c) PURCHASER'S ADDITIONAL PAYMENT UNDERTAKING. Without derogating from the
above, in the event that during the three year period commencing at the date of
the Closing the Purchaser shall sell, for cash or publicly traded securities
(excluding publicly traded securities that are received in connection with a
merger or a reorganization of the Company), at least 20% of the total number of
the Company's Ordinary Shares it had purchased at the Closing and at the Tefron
Closing, at an average price per share (adjusted for share combinations and
splits) which, together with the total amount of dividends which had been
distributed to the Purchaser with respect to each such share prior to the date
it was sold, is equal to or higher than US$9.22 (the "SALE THRESHOLD"), then, on
the third anniversary of the Closing, the Purchaser shall pay the Sellers an
amount equal to the excess of such average price per share over the Sale
threshold, but in any event not exceeding US$0.75, per each Purchased Share so
sold by the Purchaser.

     (d) The provisions of Section 1.1(c) above shall also apply to the
Purchaser's aggregate sales during the four year period commencing on the date
of the Closing; provided, however, that the Sale Threshold in such case shall be
US11.6 instead of US$9.22.

1.2 CLOSING; DELIVERIES.

The sale and purchase of the Purchased Shares shall take place at a closing (the
"CLOSING") to be held at the offices of Naschitz, Brandes & Co., 5 Tuval St.
Tel-Aviv 67897, at 10:00 AM, simultaneously with and contingent upon the closing
(the "TEFRON CLOSING") of the issue and sale by the Company to the Purchaser of
Series A Ordinary Shares of the Company pursuant to the Tefron Purchase
Agreement, in the form attached hereto as SCHEDULE 1.2.


                                       3
<PAGE>


Without derogating from the provisions of Section 4 below, at the Closing, the
following transactions shall occur, which transactions shall be deemed to take
place simultaneously and no transaction shall be deemed to have been completed
or any document delivered until all such transactions have been completed and
all required documents delivered:

          (a) each Seller shall cause the portion of the Purchased Shares being
sold by such Seller to be delivered to the Purchaser; and

          (b) the Purchaser shall deliver to each Seller, the portion of the
Purchase Price equivalent to the applicable number of Purchased Shares sold by
such Seller, by wire transfer of immediately available funds (which shall be
denominated in U.S. Dollars) to such bank account as shall be designated by each
Seller in writing.

                                   ARTICLE II

                  REPRESENTATIONS AND WARRANTIES OF THE SELLERS

Each of the Sellers, with respect to Sections 2.1 - 2.3 and 2.6, and only Arwol,
with respect to Sections 2.4 - 2.5, hereby represents and warrants to the
Purchaser (severally and not jointly) and acknowledges that the Purchaser is
entering into this Agreement and the Tefron Purchase Agreement in reliance
thereon, as follows:

2.1 AUTHORIZATION; BINDING AUTHORITY; ENFORCEABILITY.

          (a) This Agreement has been duly executed and delivered by it, and
constitutes a legal, valid and binding obligation of such Seller, enforceable
against it in accordance with its terms.

          (b) The execution of this Agreement by the Seller, the consummation of
the transactions contemplated herein, and the fulfillment of this Agreement in
accordance with its terms, will not conflict with or constitute a breach of any
agreement to which such Seller is a party and will not trigger any right of
first refusal, tag-along rights or pre-emptive rights.

2.2 OWNERSHIP; TITLE TO PURCHASED SHARES. It is the beneficial owner of the
number of Purchased Shares to be sold by it at the Closing. It represents and
warrants that at the Closing, it shall deliver to the Purchaser good title to,
and all rights to vote, all of the shares constituting its part of the Purchased
Shares, free and clear of any Encumbrances. For purposes of this Agreement, an
"ENCUMBRANCE" shall mean any form of legal or security interest of a third party
including but not limited to any lien, mortgage, pledge, charge, title
retention, right to acquire, hypothecation, option or right of first refusal.
Excluding a portion of the Purchased Shares that are being sold by Macpell,
which were purchased by Macpell on the "open market", the Purchased Shares have
not been registered under the securities laws of the United States and may only
be sold on the NYSE following such registration or pursuant to an applicable
exemption therefrom.


                                       4
<PAGE>


2.3 NO VIOLATIONS. Subject to Section 4.3 herein and except as set forth in
SCHEDULE 2.3 attached hereto, the execution, delivery and performance by the
Seller of this Agreement will not (i) violate any applicable law; (ii) require
any consents or approvals of, or filings or registrations with, any governmental
agency, or regulatory authorities or any other party to any agreement to which
such Seller is a party, which had not been received before the signing of this
Agreement; (iii) to the Seller's knowledge, result in the breach of any material
agreement or license to which the Company or any Seller is a party; or (iv) to
the Seller's knowledge, require the Company or any Seller to obtain any consents
or approvals from any governmental authority.

2.4 FINANCIAL STATEMENTS. The Purchaser has been provided with the consolidated
audited balance sheets of the Company as of December 31, 2002, and the unaudited
but reviewed financial statements for the nine month period ended September 30,
2003, and the related statements of income, cash-flow and statements of
shareholders' equity of the Company for the periods then ended, together (in the
case of the audited financial statements) with the notes thereto (the "FINANCIAL
STATEMENTS").

The Financial Statements are accurate and complete in all material respects and
present fairly the financial position of the Company as of their respective
dates and the results of operations of the Company for the periods covered
thereby. The Financial Statements have been prepared in accordance with United
States generally accepted accounting principles, consistently applied throughout
the periods covered. Since September 30, 2003, the Company's business has not
suffered any material adverse change.

2.5. COMPLIANCE WITH SECURITIES RULES AND REGULATIONS. During the two year
period immediately prior to the date hereof, the Company has timely filed all
required forms, reports and documents with the Securities Exchange Commission
(the "SEC"), each of which has complied in all material respects with all
applicable requirements of the Securities Act of 1933, as amended (the
"SECURITIES ACT") and the Securities Exchange Act of 1934, as amended (the
"EXCHANGE ACT") and the rules and regulations promulgated thereunder, each as in
effect on the dates such forms, reports and documents were filed. As of the time
it was filed with the SEC (or, if amended or superseded by a filing prior to the
date of this Agreement, then on the date of such filing): (i) each report,
registration statement (on a form other than Form S-8) and definitive proxy
statement filed by the Company with the SEC during the two year period
immediately prior to the date hereof (the "COMPANY SEC DOCUMENTS"), including,
any financial statements or schedules included or incorporated by reference
therein, complied in all material respects with the applicable requirements of
the Securities Act or the Exchange Act (as the case may be); and (ii) none of
the Company SEC Documents contained any untrue statement of a material fact or
omitted to state a material fact required to be stated therein or necessary in
order to make the statements therein, in the light of the circumstances under
which they were made, not misleading.


                                       5
<PAGE>


2.6. ALL MATERIAL INFORMATION. The representations furnished to the Purchaser in
connection with this Agreement, when taken as a whole, do not contain any untrue
statement of a material fact or omit to state a material fact necessary to make
the statements made therein, in light of the circumstances under which they were
made, not misleading.

2.7. SELLERS' UNDERTAKING.

(a) The Sellers hereby undertake to vote all of the Tefron shares held or
otherwise controlled by them in favor of the approval by the General Meeting of
Shareholders of Tefron of the Tefron Purchase Agreement and the transactions
contemplated therein.

(b)  Arwol undertakes that if, under any applicable law, Macpell shall be
required to convene a General Meeting of Shareholders for the purpose of
approving the transactions contemplated herein, it shall vote(or cause the
trustee to vote) all of the Macpell shares held or otherwise controlled by it in
the General Meeting of Shareholders of Macpell in favor of the approval of such
transactions, to the extent within its control.

                                   ARTICLE III
                   REPRESENTATIONS AND WARRANTIES OF PURCHASER

The Purchaser makes the following representations and warranties to the Sellers:

3.1 ORGANIZATION. The Purchaser is a special purpose vehicle formed for the
purpose of effecting the transactions contemplated herein and in the Tefron
Purchase Agreement.

NDMS, the general partner of the Purchaser, is wholly owned by the Delaware
Fund. NDMS has full and exclusive power to take any and all actions of behalf of
the Purchaser and to exercise all rights of the Purchaser, including but not
limited to, with respect to its interests in Tefron and its rights pursuant to
this Agreement.

FIMI 2001 Ltd., the Managing General Partner of the Israeli Fund and the
Delaware Fund, has full and exclusive power to take any and all actions on
behalf of NDMS.

3.2  AUTHORIZATION; BINDING AUTHORITY; ENFORCEABILITY.

          (a) The Purchaser has full corporate power and authority to execute
and deliver this Agreement, to perform its obligations hereunder, to consummate
the transactions contemplated hereby, and to purchase the Purchased Shares from
the Sellers pursuant to the provisions of this Agreement.

          (b) This Agreement has been duly executed and delivered by the
Purchaser, and constitutes the legal, valid and binding obligations of the
Purchaser, enforceable against the Purchaser in accordance with its terms.


                                       6
<PAGE>


3.3 NO VIOLATIONS. The execution, delivery and performance by the Purchaser of
this Agreement will not (i) violate any laws applicable to the Purchaser; (ii)
violate, conflict with, terminate, modify or constitute a breach of, or a
default under, the organizational documents of the Purchaser or any agreement to
which the Purchaser is a party or a commitment to which it is obligated; or
(iii) require any consents or approvals from any governmental agency, or
regulatory authorities or any other party to any agreement to which the
Purchaser is a Party.

3.4. The entities comprising the Fund are sophisticated investors that have
experience in business and financial matters and are capable of evaluating the
merits and risks relevant to the Company and to the transaction contemplated by
this Agreement.

3.5. The Purchaser has had adequate opportunity to ask questions and receive
answers from the Sellers and to receive such other information as it has
requested in order to evaluate the transactions contemplated herein, including,
without limitations the Financial Statements and the Company SEC Documents).The
Purchaser confirms that it has conducted legal and financial due diligence of
the Company as it deemed appropriate and has reviewed the Company's SEC filings
listed in SCHEDULE 3.5 attached hereto.

 3.6. The Purchaser is able to bear the economic risk associated with the
purchase of the Purchased Shares. The Purchaser is acquiring the Purchased
Shares for its own account for investment purposes only and not for the purpose
of distributing or reselling the Shares. The Purchaser acknowledges that in
making its decision to enter into the transactions contemplated herein, it has
not relied on any information other than the representations and warranties set
forth in this Agreement, the Tefron Purchase Agreement and public information
filed with the NYSE.

 3.7 The Purchaser understands, acknowledges and agrees that all or a portion of
the Purchased Shares have not been registered under the securities laws of any
jurisdiction, and may not be transferred without such registration or an
exemption therefrom. Until registered under the Securities Act or otherwise
permitted under the Securities Act, all certificates evidencing any of the
Purchased Shares shall bear a legend, prominently stamped or printed thereon,
reading substantially as follows:

"THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT") OR APPLICABLE
STATE SECURITIES LAWS. THESE SECURITIES HAVE BEEN ACQUIRED FOR INVESTMENT AND
NOT WITH A VIEW TO DISTRIBUTION OR RESALE, AND MAY NOT BE SOLD OR OTHERWISE
TRANSFERRED WITHOUT AN EFFECTIVE REGISTRATION STATEMENT FOR SUCH SECURITIES
UNDER THE SECURITIES ACT AND APPLICABLE STATE SECURITIES LAWS, OR THE
AVAILABILITY OF AN EXEMPTION FROM THE REGISTRATION PROVISIONS OF THE SECURITIES
ACT AND APPLICABLE STATE SECURITIES LAWS".

3.8 Nothing set forth in this Section 3 shall be deemed to detract from or
otherwise prejudice the Purchaser's reliance on the Sellers' representations and
warranties set forth in Section 2 above.


                                       7
<PAGE>


                                   ARTICLE IV

                              CONDITIONS TO CLOSING

4.1 CONDITIONS TO CLOSING OF THE PURCHASER:

The obligations of the Purchaser to purchase the Purchased Shares and transfer
the Purchase Price at the Closing are subject to Section 4.3 herein and to the
fulfillment at or before the Closing of the following conditions precedent, any
one or more of which may be waived in writing, in whole or in part, by the
Purchaser, which waiver shall be at the sole discretion of the Purchaser:

          (a) REPRESENTATIONS AND WARRANTIES. The representations and warranties
made by each of the Sellers in this Agreement shall be true and correct in all
material respects as of the Closing as if made on the date hereof.

          (b) TEFRON CLOSING. All of the terms and conditions to the closing
under the Tefron Purchase Agreement shall have been met and the Closing (as
defined therein) shall have taken place.

          (c) BOARD OF DIRECTORS. The General Meeting of shareholders of the
Company shall have approved, effective as of the Closing, the election to the
Company's seven-member Board of Directors (not including external directors), of
three members designated by the Purchaser, all in accordance with Section 5.1
below.

4.2 CONDITIONS TO CLOSING OF THE SELLERS.

The obligation of each of the Sellers to sell its part of the Purchased Shares
at the Closing is subject to Section 4.3 herein and to the fulfillment at or
before the Closing of the following condition, which may be waived in writing by
both Sellers, collectively, which waiver shall be at the sole discretion of the
Sellers:

REPRESENTATIONS AND WARRANTIES. The representations and warranties made by the
Purchaser in this Agreement shall be true and correct in all material respects
as of the Closing as if made on the date hereof.

4.3 TERMINATION

      In either of the following cases, this Agreement shall become null and
void and the parties will not have any claims against each other:

      (a)    if the Tefron Closing is not consummated within 120 days (or a
             longer period, if approved in writing by the Purchaser and the
             Sellers) from the date of this Agreement; or


                                       8
<PAGE>


      (b)    if under any applicable law Macpell shall be required to convene a
             General Meeting of Shareholders for the purpose of approving the
             transaction contemplated herein and such General Meeting does not
             approve such transactions.

             For the purpose of avoiding any doubt, it is hereby clarified that
             if such General Meeting of Shareholders of Macpell approves
             Macpell's participation in this Agreement with respect to its terms
             regarding the parties' relationship as of the Closing (Article V),
             but does not approve the sale by Macpell, pursuant to the
             provisions of this Agreement, of any of the Company's shares held
             by Macpell, then Arwol shall sell to the Purchaser the entire
             amount of the Purchased Shares, and this Agreement shall not be
             terminated by reason of this Sub-Section 4.3 (b).

                                    ARTICLE V

The parties to this Agreement (each shall be referred to in this Section 5 as a
"SHAREHOLDER" and, collectively, the "SHAREHOLDERS") agree that concurrently
with, and subject to, the Closing, the provisions contained in this Article V
shall become effective and shall remain in effect throughout the term defined in
Section 5.10 herein. The Sellers acknowledge that the Purchaser is entering into
this Agreement and the Tefron Purchase Agreement in reliance on the
implementation of the provisions contained in this Article V.

5.1. BOARD OF DIRECTORS

          (a) The Shareholders hereby agree to vote all of the Series A Ordinary
Shares of the Company (the "ORDINARY SHARES") now or hereafter owned or
controlled by them (including without limitation, Ordinary Shares owned by them
upon exercise of any options or warrants to purchase Ordinary Shares or other
convertible securities of the Company or upon conversion of convertible
securities of the Company into Ordinary Shares), whether beneficially or
otherwise held by them, for the election to the Company's Board of Directors of:
(i) three members (of whom at least one shall be female and at least one shall
qualify as an "Independent Director" as such term is defined under the rules
applicable to companies listed on the NYSE) and, subject to applicable law and
as of the Company's first Annual General Meeting in 2004 - one external
director, that shall be designated by the Purchaser, (ii) three members (of whom
at least one shall qualify as an Independent Director and shall qualify as a
"Financial Expert" (as such term is defined under the rules applicable to
companies listed on the NYSE) and, subject to applicable law and as of the
Company's first Annual General Meeting in 2004 - one external director, that
shall be designated by the Sellers, and (iii) the Company's Chief Executive
Officer.


                                       9
<PAGE>


      It is hereby agreed between Macpell and Arwol with respect to
sub-paragraph (ii) above, that the Sellers' nominees for directors shall be
chosen and divided between the Sellers as follows: (a) each of the Sellers shall
have the right to choose such number of nominees which bears the same ratio to
the total number of the Sellers' nominees (as described in said sub-paragraph
(ii)), as the ratio that the number of its Ordinary Shares bears to the total
number of Ordinary Shares held by both Sellers (with respect to Arwol - rounded
down to the nearest whole number of nominees, but not less than one nominee; and
with respect to Macpell - rounded up to the nearest whole number of nominees,
but not less than one nominee) ; (b) notwithstanding sub-paragraph (a) above, if
the number of Ordinary Shares held by one of the Sellers is equal or greater
than five times the number of Ordinary Shares held by the other Seller, the
latter will have no right to choose a nominee, and all of the Sellers' nominees
shall be chosen by the first.

      It is hereby clarified that the Sellers may decide (subject to any
approval required under applicable law) to change their nominees' allocation
mechanism described in the immediately preceding paragraph, without the need for
any approval from the Purchaser. For the purpose of Section 5.1(a)(ii) herein,
the Purchaser shall be bound to act (vote) only according to a written notice
signed by both Macpell and Arwol.

          (b) The Shareholders confirm that the Company's Chairman, Mr. Arie
Wolfson, has agreed to remain in office until the Company's first Annual General
Meeting of Shareholders in calendar year 2005 (which General Meeting of
Shareholders shall be convened by no later than July 31, 2005). Subject to the
provisions of applicable law, on or before such Annual General Meeting of
Shareholders the Shareholders shall endeavor to agree on the identity of the
Chairman as of and following such Annual General Meeting of Shareholders;
PROVIDED, HOWEVER, that in the event that the Shareholders are unable to agree
on the identity of the Chairman, each of the Purchaser and the Sellers (taken as
a group) shall each be entitled to designate the Chairman for an 18 month
period, provided that the Purchaser shall be the first to exercise such right
for a period commencing on and as of the Company's first Annual General Meeting
of Shareholders in calendar year 2005.

          (c) The Shareholders shall appoint an Executive Committee for
consultation purposes, which shall comprise of Messrs. Arie Wolfson and Ishay
Davidi or, in the event any of them cannot fulfill such duty, an alternate
member will be appointed by the Sellers (if Arie Wolfson can not fulfill his
duties) or the Purchaser (if Ishay Davidi cannot fulfill his duties). For the
avoidance of doubt, the Executive Committee is not a committee of the Company
and may not bind the Company in any way.

          (d) No Shareholder, or any officer, director, shareholder or employee
of such Shareholder, makes any representation or warranty as to the fitness or
competence of the nominee of any other party to this Agreement to the Company's
Board of Directors by virtue of its execution of this Agreement or by voting in
accordance with the provisions of this Agreement. For the avoidance of doubt,
each Shareholder (and the directors designated by it) shall be solely
responsible for the compliance of its designee(s) with the requirements of
applicable law relating to director's competency (including, without
limitations, the provisions of Sections 226, 227 and 228 of the Companies Law,
1999 (the "COMPANIES LAW").


                                       10
<PAGE>


          (e) In the event of any share split, share dividend, recapitalization,
reorganization or combination, the provisions of this Agreement shall apply also
to any Ordinary Shares issued to the Shareholders with respect to, or in
replacement of, their shareholdings in the Company prior to such act.

5.2. RIGHT OF FIRST OFFER; TAG-ALONG

          (a) If a Shareholder (the "SELLING PARTY") wishes to sell or otherwise
transfer Ordinary Shares of the Company, such Shareholder shall be required to
first make an offer to the other Shareholders (the "OFFEREES"), as set forth
below.

          (b) The Selling Party shall send the Offerees a written offer in which
the Selling Party shall specify the following information (the "OFFER"): (i) the
number of Ordinary Shares that the Selling Party proposes to sell or transfer
(the "OFFERED SHARES"); (ii) a representation and warranty that the Offered
Shares shall be, at the time of their transfer, free and clear of Encumbrances;
and (iii) the price that the Selling Party intends to receive in respect of the
Offered Shares, which shall be stated in cash, together with the requested terms
of payment thereof; (iv) the identity of the prospective purchaser or
transferee, if any. The Offer shall constitute an irrevocable offer made by the
Selling Party to sell to the Offerees the Offered Shares or to have such
Offerees participate in such sale, all upon the terms specified in the Offer and
as described below.

          (c) If the Offer specifies that it is contingent upon the purchase of
all of the Offered Shares, the Selling Party shall be entitled to refuse to
transfer the Ordinary Shares pursuant to the Offer to the Offerees if the
Offerees do not wish to purchase all of the Offered Shares.

          (d) Each Offeree will notify the Selling Party within 10 business days
of receipt of the Offer whether it (i) wishes to purchase all or any portion of
the Offered Shares, or (ii) wishes to participate in the sale to a proposed
purchaser specified in the Offer or, if there was no proposed purchaser at the
time of the Offer, any other third party. If an Offeree did not give such notice
electing any of the above (i) or (ii) alternatives, such Offeree shall be deemed
to have notified that it does not wish to either buy the Offered Shares or
participate in the sale thereof. In case that according to the Offerees'
notifications, they wish to purchase more than the entire amount of the Offered
Shares and they do not reach an agreement on the allocation of such Offered
Shares, each Offeree shall be entitled to purchase its pro rata share of the
Offered Shares. Each Offeree's pro rata share of the Offered Shares shall be a
fraction, of which the number of Ordinary Shares of the Company owned by such
Offeree on the date of the Offer shall be the numerator and the total number of
Ordinary Shares of the Company held (on such date of the Offer) by all Offerees
who wish to purchase the Offered Shares shall be the denominator.


                                       11
<PAGE>


          (e) If one or more of the Offerees agrees to purchase the Offered
Shares on the terms specified in the Offer, the Offered Shares shall become the
property of the Offeree(s) against payment of the consideration as specified in
the Offer. If there remain any Ordinary Shares that have not been acquired by
the Offerees and the Selling Party has not exercised its right to refuse to
transfer any of the Offered Shares pursuant to the Offer (as set forth in
sub-section (c) above), then subject to the Offerees' rights under sub-section
(f) below, the Selling Party may sell such Ordinary Shares or, if it has
exercised its right under sub-section (c) above, all Offered Shares, the
proposed purchaser specified in the Offer or, if there was no proposed purchaser
at the time of the Offer, any other third party, provided that such sale is
consummated (i) in a bona fide transaction within a 90 day period (ii) at a
price that is not lower than that specified in the Offer; (iii) subject to
payment terms that are no more favorable to the purchaser than those specified
in the Offer, and (iv) provided that, unless the sale is consummated by means of
"market trade", the transferee of the Offered Shares shall acknowledge in
writing that it agrees to be bound by the provisions of this Section 5, as if it
were an original party to this Agreement.

          (f) If an Offeree does not wish to accept the Offer but wishes to sell
or otherwise transfer any or all of such Offeree's Ordinary Shares together with
the Offered Shares being sold by the Selling Party, the Offeree (the "TAG ALONG
SHAREHOLDER") shall, during such 10 business day period, have the right to
notify the Selling Party of its intention to exercise its Tag Along Right
pursuant to this sub-section (f) (the "TAG ALONG NOTICE"). Following the Tag
Along Notice, the Tag Along Shareholder shall add to the Ordinary Shares being
sold by the Selling Party to such proposed purchaser (the "PROPOSED PURCHASER")
that number of Ordinary Shares which bears the same ratio to the total number of
Ordinary Shares held by the Tag Along Shareholder, as the ratio that the number
of the Offered Shares bears to the Selling Party's total number of Ordinary
Shares of the Company, and upon the same terms and conditions under which the
Selling Party's Ordinary Shares shall be sold. In the event that the Tag Along
Shareholder exercises its rights hereunder, the Selling Party must cause the
Proposed Purchaser to add such Ordinary Shares to the Offered Shares to be
purchased by the Proposed Purchaser, as part of the sale agreement, or reduce
the number of Ordinary Shares that it proposes to sell to the Proposed Purchaser
(in which case, the Selling Party and any Tag Along Shareholder will contribute
the identical portion of Ordinary Shares relative to their total shareholdings
in the Company), and either conclude the transaction in accordance with such
revised structure or withdraw from completing the transaction. Notwithstanding
the foregoing, in the event that the exercise of the Tag-Along Right by an
Offeree would result in such Offeree's non-compliance with the restrictions set
forth in Sections 103 or 104 of the Israeli Tax Ordinance, to the extent then
applicable to it, then, in lieu of participation in the proposed sale of Company
shares to the Proposed Purchaser, such Offeree shall be entitled to sell on a
later date, such number of Company shares which the Offeree would have been
entitled to add to the Offered Shares sold to the Proposed Purchaser, and the
restrictions on transfer set forth in this Section 2 shall not apply to such
sale.


                                       12
<PAGE>


          (g) Notwithstanding the foregoing, the provisions of this Section 5.2
shall not apply to any transfer of Ordinary Shares by a Shareholder to its
Permitted Transferees (provided that such Permitted Transferee shall acknowledge
in writing that it agrees to be bound by the provisions of this Section 5, as if
it were an original party to this part of the Agreement) nor to any transfer
from Macpell to Arwol or from Arwol to Macpell. For purposes of this Agreement,
the term "PERMITTED TRANSFEREES" shall mean (i) a transferee by operation of
law; (ii) in the case of a transfer by a Selling Party that is an investment
fund, any affiliated fund managed by the same general partner or management
company or by an affiliate thereof and/or the investors of such investment fund,
(iii) an entity controlled by, controlling, or under common control with the
Selling Party or any person set forth in (i) - (iii); (iv) an individual (and/or
any of his immediate family members) controlling the Selling Party or any person
set forth in (i) - (iii); and (v) a transferee in a swap (or substantially
similar) transaction according to which the Selling Party receives shares of
Macpell as consideration for Ordinary Shares in Tefron, in a manner that its
holdings in Tefron, directly, and indirectly through Macpell, are not materially
reduced.

          (h) Notwithstanding anything to the contrary, any transfer of Company
shares by a Shareholder to any direct competitor of the Company or to any entity
that is a "Controlling Shareholder" (as such term is defined in the Companies
Law) of a direct competitor of the Company, will require the prior written
consent of each of the other Shareholders.

          (i) Notwithstanding the above, the sale by each of the Purchaser and
the Sellers (taken as a group), in one or more instances, of shares of the
Company constituting in the aggregate less than 2.7% of the Company's issued and
outstanding share capital, shall not be subject to any of the restrictions on
transfer set forth in this Section 2.

          (j) Notwithstanding the above, in the event that a banking institution
realizes its pledge over Ordinary Shares of the Company held by a Shareholder
and wishes to sell any or all of such shares, the other Shareholders, whose
Ordinary Shares of the Company are not being sold by such banking institution,
shall not be granted the Right of First Offer set forth in Sections 5.2(a)-(e)
above or the Tag-Along Right set forth in Section 5.2(f) above with respect to
such shares.

          (k) The restrictions set forth above shall also apply to a sale or
other disposition of limited partnership interests in the Purchaser if,
following such sale or disposition, the Fund would beneficially hold less than
50% of the aggregate partnership interests in the Purchaser or FIMI 2001 Ltd.
shall no longer control the Purchaser.

5.3. DRAG ALONG

Notwithstanding anything to the contrary set forth in this Section 5, in
the event that any of the Shareholders ("DRAG ALONG INITIATOR") secures a bona
fide offer from any third party, in cash or publicly traded securities, to
purchase all of the Ordinary Shares then held by, in cash or publicly traded
securities, at a price per share (adjusted for allocation of dividend, bonus
shares, splits etc.) of not less than US$10, provided that such price per share
shall not be lower than 80% of the average of the closing prices of the
Company's shares on the NYSE over the consecutive 60 trading days immediately
preceding such sale, and the offeror conditions its offer on the acquisition of
all the shares held by all of the other Shareholders at such time, such
Shareholders will be required (subject to the provisions of the following
paragraph), if so demanded by the Drag Along Initiator, to sell all of the
shares of the Company then held by them to such offeror, at the same price and
upon the same terms and conditions as those to which the sale by the Drag Along
Initiator is subject. Notwithstanding the foregoing, in lieu of selling the
shares, as demanded by the Drag Along Initiator, the other Shareholder(s) may
acquire all of the Company's shares then held by the Drag Along Initiator at the
price per share and upon the same terms and conditions as those to which the
sale to the offeror would have been subject; PROVIDED, HOWEVER, that such
acquisition of Company shares by the other Shareholder(s) shall be for cash only
(and, if the consideration offered by the offeror is shares of a publicly traded
entity, such shares shall be valued in accordance with the average closing price
of such shares on the principal stock exchange on which they are traded over the
30 day period prior to such demand) and such cash amount shall be delivered to
the Drag Along Initiator within 10 business days following its demand.


                                       13
<PAGE>


For the avoidance of doubt, an offer shall not be deemed bona fide if the Drag
Along Initiator or any of its controlling parties is a "Baal Inyan" (as such
term is defined in the Companies Law) in such third party or in the publicly
traded entity whose shares are offered as consideration.

5.4. DISCUSSIONS PRIOR TO MEETINGS.

The Shareholders shall meet regularly and in any event prior to each General
Meeting of shareholders of the Company and will review, discuss and attempt to
reach a unified position with respect to principal issues on the agenda of each
such meeting such as approval of any merger or acquisition, sale of all or
substantially all of the Company's assets, etc. For the sake of avoiding any
doubt, it is hereby clarified that this Section 5.4 shall not be interpreted as
forcing any Shareholder to act or vote according to any position stated at such
prior meeting, even if such position is acceptable to the other Shareholders
(and even if such other Shareholders hold the majority of the Ordinary Shares).

5.5. DIVIDEND DISTRIBUTION.

The Shareholders shall formulate a mutually agreeable dividend distribution
policy for the Company, which policy shall provide for the distribution of an
annual amount, net after taxes (including withholding tax), of at least US$ 2
million with respect to calendar year 2004, and at least US$4.5 million,
effective as of calendar year 2005, and shall utilize their best efforts to
cause the Company to adopt such policy, subject to: (a) the provisions of
applicable law (including NYSE requirements); (b) any undertaking and commitment
made or to be made towards banks and other creditors; (c) the decision of the
Company's Board of Directors, taking into account the Company's financial needs,
investments and all other relevant aspects.

5.6. NO AGREEMENTS WITH OTHER SHAREHOLDERS OF THE COMPANY.

Excluding this Agreement, each Shareholder shall be prohibited from entering
into any Stockholders Agreement (as defined herein) with any shareholder of the
Company other than with any of the Shareholders; provided, however, that this
Agreement shall prevail over any other agreement among any of the Shareholders.

For this Section 5.6, "Stockholders Agreement" means a voting or similar
agreement, or any agreement relating to the exercise of voting rights in the
Company, or any similar undertaking or commitment (including a unilateral
commitment), whether in the form a written instrument or otherwise.


                                       14
<PAGE>


5.7. MANAGEMENT FEE. The Shareholders hereby agree to vote all of the Ordinary
Shares of the Company now or hereafter owned or controlled by them, whether
beneficially or otherwise held by them, in order to cause the Company (i) to pay
the Purchaser (or any of its affiliates) the Management Fees (as more fully set
forth in the Tefron Purchase Agreement), and (ii) as of the date on which Arie
Wolfson no longer serves as the Chairman of the Company's Board of Directors
(the "CHAIRMAN"), to pay Arie Wolfson or his designees for their services to the
Company, an aggregate annual amount of $120,000.

5.8. PURCHASE OF SHARES FROM DISCOUNT INVESTMENT COMPANY LTD.("DISCOUNT"). Any
Shareholder (the "ACQUIRING PARTY") wishing to purchase Ordinary Shares of the
Company from Discount shall be required to offer, in writing, to the other
Shareholders to participate in such purchase, at the price per share and upon
the same terms and conditions applicable to the purchase of Company shares by
the Acquiring Party. Each Shareholder will notify the Acquiring Party within 7
business days of its receipt of such offer if it wishes to participate in such
purchase, and to purchase its pro rata portion of the Company shares to be
purchased from Discount. In the event that a Shareholder does not provide the
Acquiring Party with a written notice within such 10 day period, such
Shareholder shall be deemed to have waived its right to participate in such
purchase.

5.9. Notwithstanding anything to the contrary herein, the parties acknowledge
that 3,588,210 Ordinary Shares of the Company owned by Macpell (the "PLEDGED
SHARES") are subject to a pledge created for the benefit of Bank Hapoalim B.M
pursuant to that certain Deed of Pledge dated June 17, 2003 and, accordingly,
the Pledged Shares were transferred and are registered in the name of Poalim
Trust Services Ltd., the trust company of Bank Hapoalim B.M. (collectively, the
"BANK"). Pursuant to the terms of such pledge, upon the occurrence of certain
conditions, the Bank will be free to vote the Pledged Shares and shall not be
bound by the provisions of this Article V.

5.10. TERM OF ARTICLE V.

      (a)    The provisions of this Article V shall remain in effect until the
             fifth anniversary of the Closing.

      (b)    Notwithstanding the above, the Purchaser shall cease to have any
             rights or privileges under this Article V as of the first date on
             which the Purchaser holds less than 10% of the Company's issued
             share capital (on a non-diluted basis), and shall cease to bear any
             obligation or duty under this Article V as of the first date on
             which the Purchaser holds less than 5% of the Company's issued
             share capital (on a non-diluted basis);

      (c)    Notwithstanding the above, the Sellers shall cease to have any
             rights or privileges under this Article V as of the first date in
             which the Sellers hold (in the aggregate) less than 10% of the
             Company's issued share capital (on a non-diluted basis), and each
             Seller shall cease to bear any obligation or duty under this
             Article V as of the first date on which such Seller holds less than
             5% of the Company's issued share capital (on a non-diluted basis).


                                       15
<PAGE>


                                   ARTICLE VI

                                  MISCELLANEOUS

6.1. TAXES; COMMISSIONS. Any sales, stamp or transfer tax due upon the sale of
any Purchased Shares by the Sellers to the Purchaser under this Agreement shall
be borne by the Sellers (taken as a group) and the Purchaser in equal parts. In
the event that Macpell sells to the Purchaser Ordinary Shares of the Company
constituting less than 50% of the Offered Shares, the portion of expenses to be
borne by the Sellers, shall be borne by Arwol and Macpell on a pro rata basis.

6.3. EXPENSES. Each party hereto shall pay its own expenses in connection with
the negotiation and preparation of this Agreement and the related agreements and
the consummation of the transactions contemplated hereby and thereby; provided,
however, that if the Closing is effected, then at the Closing, each of the
Sellers shall pay one half of the Purchaser's fees and expenses described above
in an amount of US$17,000 plus VAT (i.e. an aggregate of US$34,000 plus VAT by
both Sellers).

6.4. SURVIVAL OF REPRESENTATIONS. All representations and warranties made by any
party in this Agreement shall survive the Closing and be in effect until the
termination of eighteen (18) months following the Closing Date, and following
such 18 month period, the representations and warranties shall expire and be of
no further force or effect.

6.5 NOTICES. All notices required or permitted hereunder to be given to a party
pursuant to this Agreement shall be in writing and shall be deemed to have been
duly given to the addressee thereof (i) if hand delivered, on the day of
delivery, (ii) if given by facsimile transmission, on the business day on which
such transmission is sent and confirmed, (iii) if mailed by registered mail,
return receipt requested, five business days following the date it was mailed,
to such party's address as set forth below or at such other address in Israel as
such party shall have furnished to each other party in writing in accordance
with this provision:

      If to Macpell: Macpell Industries Ltd.
                     28 Chida Street
                     Bnei Brak 51371
                     Israel
                     Facsimile:+972-3-6189868
                     with a copy to:


                                       16
<PAGE>


                     Dror Brandwein, Adv.
                     Meitar, Liquornik, Geva & Leshem Brandwein.
                     16 Abba Hillel Street,
                     Ramat Gan

                     Israel
                     Facsimile: +972-3-6103111

      If to Arwol:   Arwol Holdings Ltd.
                     At: Volovelsky, Dinstein, Sneh & Co., Law Offices
                     Attn.: Mr. Pinhas Volovelsky, Adv.
                     14 Shenkar Street
                     Herzlia Pituach 46733
                     Israel
                     Facsimile: +972-9-9589695

      If to the Purchaser:

                     N.D.M.S Ltd.
                     c/o FIMI 2001 Ltd.
                     "Rubinstein House"
                     37 Petach Tikva Road
                     Tel: 03-5652244
                     Fax: 03-5652245


      With a copy to:

                     Sharon A. Amir
                     Nascitz, Brandes & Co.
                     5 Tuval Street, Tel-Aviv 67897
                     Israel
                     Tel:03-6235073/76
                     Fax:03-6235021

6.6 WAIVER. Any waiver hereunder must be in writing, duly authorized and signed
by the party to be bound, and shall be effective only in the specific instance
and for the purpose for which it was given. No failure or delay on the part of
any Seller or the Purchaser in exercising any right, power or privilege under
this Agreement shall operate as a waiver thereof, nor shall any single or
partial exercise of any right, power or privilege hereunder preclude any other
or further exercise thereof or the exercise of any other right, power or
privilege.


                                       17
<PAGE>


6.7 ENTIRE AGREEMENT. This Agreement, the exhibits and the schedules hereto
constitute the entire agreement among the parties hereto and supersede any other
agreement that may have been made or entered into by any Seller or the Purchaser
relating to the transactions contemplated by this Agreement.

6.8 AMENDMENTS. This Agreement may be amended or modified in whole or in part
only by a duly authorized written agreement that refers to this Agreement and is
signed by the parties hereto.

6.9 LIMITATIONS ON RIGHTS OF THIRD PARTIES. Nothing expressed or implied in this
Agreement is intended or shall be construed to confer upon or give any person,
other than the Sellers and the Purchaser, any rights or remedies under this
Agreement.

6.10 CAPTIONS PREAMBLE, AND EXHIBITS. The captions in this Agreement are
inserted for convenience of reference only and shall not be considered a part of
or affect the construction or interpretation of any provision of this Agreement.
The Preamble, Schedules and Exhibits are an integral and inseparable part of
this Agreement.

6.11 COUNTERPARTS. This Agreement may be executed in counterparts and by
facsimile signature, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.

6.12 GOVERNING LAW; DISPUTE RESOLUTION. This Agreement shall be governed by, and
construed and enforced in accordance with, the laws of the State of Israel. Any
dispute arising under or with respect to this Agreement shall be resolved
exclusively in the appropriate court in Tel Aviv, Israel.

6.13 FURTHER ASSURANCES. The parties hereto shall execute and deliver such
additional documents and shall take such additional actions (including without
limitation procuring such resolutions or regulatory approvals) as may be
reasonably necessary or appropriate to effect the provisions and purposes of
this Agreement and the consummation of the transactions contemplated hereby.

6.14 SEVERABILITY. If any provision of this Agreement is held by a court of
competent jurisdiction to be unenforceable under applicable law, then such
provision shall be excluded from this Agreement and the remainder of this
Agreement shall be interpreted as if such provision were so excluded and shall
be enforceable in accordance with its terms; provided, however, that in such
event this Agreement shall be interpreted so as to give effect, to the greatest
extent consistent with and permitted by applicable law, to the meaning and
intention of the excluded provision as determined by such court of competent
jurisdiction.

6.15 MANNER OF PAYMENT. All payments that are paid pursuant to this Agreement
shall be paid in U.S. Dollars to each party's respective bank accounts, as shall
be designated by or on behalf of such party from time to time. All payments
shall be made by initiating such payments on a banking day, before 11.00 a.m.,
Israel time, by bank wire transfer in immediately available funds, marked for
attention as indicated.


                                       18
<PAGE>


6.15 SUCCESSORS AND ASSIGNS;

Except as otherwise expressly stated to the contrary herein, each of the parties
hereto shall not assign or transfer any of its rights or obligations hereunder
without the written consent of the other parties and the provisions hereof shall
inure to the benefit of, and be binding upon, the successors, assigns under law
("HA'AVARA AL PI DIN"), heirs, executors, and administrators of the parties.

6.16 HEITER ISKA. Wherever this Agreement, or any other future agreement between
the parties hereto, refers to loans and/or interest rates, such agreements will
be subject to Heiter Iska, under the customary terms used for that purpose in
Israeli banks.


              [THE REMAINDER OF THIS PAGE INTENTIONALLY LEFT BLANK]


                                       19
<PAGE>


      IN WITNESS WHEREOF, Macpell, Arwol and the Purchaser have each caused
this Agreement to be duly executed as of the date first above written.



Arwol Holdings Ltd.
By: /s/Arie Wolfson
    ---------------------------------
Name    Arie Wolfson
      -------------------------------
Title: Chairman of the Board
      -------------------------------

Macpell Industries Ltd.
By: /s/ Arie Wolfson / /s/ Eli Azriel
    ---------------------------------
Name:   Arie Wolfson / Eli Azriel
      ---------------------------------

Title: Chairman of the Board / Controller
      ------------------------------------

Norfet, Limited Partnership

By: /s/ Ishay Davidi
    ---------------------------------
Name:     Ishay Davidi
      -------------------------------
Title:
      -------------------------------