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Fiber diffraction dada from polymers are sufficiently different in kind and quantity from single crystal data as to warrant analyses with a different emphasis: refinement of competing molecular models where torsion angles and bond angles are the explicit variables rather than atomic coordinates. The first linked-atom least-squares (lals) refinement program had been devolved at Arnott''s laboratories at King''s College London [Arnott, S., Wonacott, A.J., 1966a. Polymer 7, 157] on mainframe and several revised versions were maintained at Purdue University [Smith, P.J.C., Arnott, S., 1978. Acta Crystallogr. Sect. A 34, 3; Chandrasekan, R. 2000. lals Users Manual, Whistler Centre for Carbohydrate Researchm Purdue University, West Lafayette, IN] on workstation. Today the lals users have to choose correctly any one program that they want to use, trigonometric or Bessel functions, from some versions. To develop a new winlals program based on the dimensioned version of the latest lals2000 program [lals Users Manual (2000)], we reviewed all the mathematical expressions and corrected the optimization of the non-bonded atomic contact terms. The winlals is coded with fortran 90 and runs on microsoft-windows PCs and the many amendments including changing input/output assignments, expanding array sizes, arranging that the update files have all output parameters of each cycle, and correcting several bugs are performed. This paper describes the mathematical expressions in detail employed in winlals and compares results of its applications obtained with those obtained earlier. [Copyright &y& Elsevier]