**UNITED
      STATES**


**SECURITIES
      AND EXCHANGE COMMISSION**


**WASHINGTON,
      D.C. 20549**


**FORM
      10-K**


(Mark
      One)


x
            ANNUAL
                REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
                ACT OF
                1934




For
      the
      fiscal year ended   **December
      31** , **2005**


OR


o
            TRANSITION
                REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
                ACT OF
                1934




For
      the
      transition period from ___________________ to __________________.




Commission
      file number  **333-115371-08**




**POPULAR
      ABS, INC.**





**(as
      depositor under a certain Pooling and Servicing Agreement dated as of August
      1,
      2005,**


**providing
      for the issuance of Mortgage Pass-Through Certificates, Series
      2005-4)**


(Exact
      name of registrant as specified in its charter)


**Delaware**
            
            **52-2029487**(State
                or other jurisdiction of
              incorporation
                or organization)
            
            (I.R.S.
                Employer
              Identification
                No.)**103
                Springer Building, 3411 Silverside Road,**
              **Wilmington,****Delaware**
            
            **19803**(Address
                of principal executive offices)
            
            (Zip
                Code)




Registrant’s
      telephone number, including area code:  **(302)
      478-6160**




Securities
      registered pursuant to Section 12(b) of the Act: **None**




Securities
      registered pursuant to Section 12(g) of the Act: **None**





Indicate
      by check mark if the registrant is a well-known seasoned issuer, as defined
      in
      Rule 405 of the Securities Act.


Yes o No x





Indicate
      by check mark if the registrant is not required to file reports pursuant to
      Section 13 or Section 15(d) of the Act.


Yes o No x


Indicate
      by check mark whether the registrant (1) has filed all reports required to
      be
      filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
      the
      preceding 12 months (or for such shorter period that the registrant was required
      to file such reports), and (2) has been subject to such filing requirements
      for
      the past 90 days. Yes x No **** * ****




***
      The closing date for the transaction was August 25, 2005.**




Indicate
      by check mark if disclosure of delinquent filers pursuant to Item 405 of
      Regulation S-K (Sec. 229.405 of this chapter) is not contained herein, and
      will
      not be contained, to the best of registrant’s knowledge, in definitive proxy or
      information statements incorporated by reference in Part III of this Form 10-K
      or any amendment to this Form 10-K. o **Not
      applicable**





Indicate
      by check mark whether the registrant is a large accelerated filer, an
      accelerated filer, or a non-accelerated filer. See definition of “accelerated
      filer and large accelerated filer” in Rule 12b-2 of the Exchange Act. (Check
      one):





Large
      accelerated filer o   Accelerated
      filer o   Non-accelerated
      filer x





Indicate
      by check mark whether the registrant is a shell company (as defined in Rule
      12b-2 of the Act). Yes o No  x




State
      the
      aggregate market value of the voting and non-voting common equity held by
      non-affiliates computed by reference to the price at which the common equity
      was
      last sold, or the average bid and asked price of such common equity, as of
      the
      last business day of the registrant's most recently completed second fiscal
      quarter.





**Not
      applicable**




Indicate
      the number of shares outstanding of each of the registrant’s classes of common
      stock, as of the latest practicable date.




**Not
      applicable**










This
      Annual Report on Form 10-K is filed by Popular ABS, Inc. (the “Reporting
      Person”) on behalf of Popular ABS, Inc. Mortgage Pass-Through Certificates,
      Series 2005-4 Trust (the “Trust”) established pursuant to that certain Pooling
      and Servicing Agreement (the “Pooling and Servicing Agreement”) dated as of
      August 1, 2005 by and among the Reporting Person, as depositor, Equity One,
      Inc., as servicer (the “Servicer”), JPMorgan Chase Bank, N.A., as trustee (the
“Trustee”), and the various sellers signatory thereto, for the issuance of the
      Popular ABS, Inc. Mortgage Pass-Through Certificates, Series 2005-4 (the
“Certificates”).




**PART
      I**




**ITEM
      1. BUSINESS**




Omitted
      pursuant to First Union Residential Securitization Transactions, Inc., SEC
      No-Action Letter (April 1, 1997) (the “No-Action Letter”).




**ITEM
      1A. RISK FACTORS**




Not
      applicable.




**ITEM
      1B. UNRESOLVED STAFF COMMENTS**




Not
      applicable.




**ITEM
      2. PROPERTIES**




Pursuant
      to the No-Action Letter, the following represents relevant information regarding
      real estate owned by the Trust:





As
      of
      December 31, 2005, the Trust owned no real estate.







**ITEM
      3. LEGAL PROCEEDINGS**




The
      Reporting Person knows of no material pending legal proceedings involving the
      Trust or the Trustee, the Servicer or the registrant with respect to the Trust,
      other than routine litigation incidental to the duties of the respective parties
      under the Pooling and Servicing Agreement. ****




**ITEM
      4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS**




None.







**PART
      II**




**ITEM
      5. MARKET FOR REGISTRANT’S COMMON EQUITY AND RELATED STOCKHOLDER
      MATTERS**




(a)
            No
                established public trading market for the Certificates
                exists.




(b)
            As
                of December 31, 2005, the number of holders of record of the publicly
                offered Certificates was 52.




(c)
            Omitted
                pursuant to the No-Action Letter.




**ITEM
      6. SELECTED CONSOLIDATED FINANCIAL DATA**




Omitted
      pursuant to the No-Action Letter.




**ITEM
      7. MANAGEMENT’S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS OF
      OPERATIONS**




Omitted
      pursuant to the No-Action Letter.




**ITEM
      7A. QUANTITATIVE AND QUALITATIVE DISCLOSURE ABOUT MARKET
      RISK**




Not
      applicable.




**ITEM
      8. FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA**




Omitted
      pursuant to the No-Action Letter.




**ITEM
      9. CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING AND FINANCIAL
      DISCLOSURE.**




None.





**ITEM
      9A. CONTROLS AND PROCEDURES**





Not
      applicable.





**ITEM
      9B. OTHER INFORMATION**





None.





**PART
      III**




**ITEM
      10. DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT**




Omitted
      pursuant to the No-Action Letter.




**ITEM
      11. EXECUTIVE COMPENSATION**




Omitted
      pursuant to the No-Action Letter.




**ITEM
      12. SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT AND RELATED
      STOCK HOLDER MATTERS**




Item
      201(d) of Regulation S-K




None.




Item
      403 of Regulation S-K




(a)
            Not
                applicable.




(b)
            Not
                applicable.




(c)
            Not
                applicable.




**ITEM
      13. CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS**




(a)
            Not
                applicable.




(b)
            Not
                applicable.




(c)
            None.




(d)
            None.





**ITEM
      14. PRINCIPAL ACCOUNTING FEES AND SERVICES.**





Not
      applicable.





**PART
      IV**




**ITEM
      15. EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM
      8-K**




(a)
            Exhibits




31.1
            Certification
                pursuant to Securities Exchange Act Rules 13a-14 and 15d-14 as adopted
                pursuant to Section 302 of the Sarbanes-Oxley Act of 2002.





99.1
            Annual
                Independent Accountants’ Servicing Report concerning servicing activities
                under the Pooling and Servicing Agreement for the Servicer’s fiscal year
                ended November 30, 2005, in accordance with the No-Action Letter.




99.2
            Annual
                Statement of Compliance under the Pooling and Servicing Agreement
                for the
                Servicer’s fiscal year ended November 30, 2005, in accordance with the
                No-Action Letter.




99.3
            Aggregate
                Statement of Principal and Interest Distributions to Certificateholders.




(b)
            See
                Item 15(a) above.





(c)
            Omitted
                pursuant to the No-Action Letter.










**SIGNATURES**




Pursuant
      to the requirements of Section 13 or 15(d) of the Securities Exchange Act of
      1934, the Reporting Person has duly caused this report to be signed on its
      behalf by the undersigned, thereunto duly authorized.




POPULAR
                ABS, INC.,
              on
                behalf of the TrustDate: March
              13, 2006
            By:
            /s/ James
              H.
              JenkinsJames
              H. Jenkins, Executive Vice President and
              CFO




SUPPLEMENTAL
      INFORMATION TO BE FURNISHED WITH REPORTS FILED PURSUANT TO SECTION 15(d) OF
      THE
      ACT BY REGISTRANTS WHICH HAVE NOT REGISTERED SECURITIES PURSUANT TO SECTION
      12
      OF THE ACT




(a)(1)  No
      annual
      report is provided to the Certificateholders other than with respect to
      aggregate principal and interest distributions.




(a)(2)  No
      proxy
      statement, form of proxy or other proxy soliciting material has been sent to
      any
      Certificateholder with respect to any annual or other meeting of
      Certificateholders.







**INDEX
      TO EXHIBITS**




Exhibit
              Number
            Description




31.1
            Certification
                pursuant to Securities Exchange Act Rules 13a-14 and 15d-14 as adopted
                pursuant to Section 302 of the Sarbanes-Oxley Act of
                2002.





99.1
            Annual
                Independent Accountants’ Servicing Report concerning servicing activities
                under the Pooling and Servicing Agreement for the Servicer’s fiscal year
                ended November 30, 2005, in accordance with the No-Action
                Letter.





99.2
            Annual
                Statement of Compliance under the Pooling and Servicing Agreement
                for the
                Servicer’s fiscal year ended November 30, 2005, in accordance with the
                No-Action Letter.





99.3
            Aggregate
                Statement of Principal and Interest Distributions to
                Certificateholders.