A polarimetric experimental method was developed to determine the Jones matrix elements of transparent optical materials without sign ambiguity. A set of polarization dependent transmittance data of the samples was measured with polarizer - sample - analyzer system and another set of data was measured with polarizer - sample - quarter-wave plate - analyzer. Two data sets were compared and mathematically analyzed to obtain the correct signs of the elements of the matrix. The Jones matrix elements of a quarter-wave plate were determined to check the validity of the method. The experimentally obtained matrix elements of the quarter-wave plate were consistent with the theoretical expectations. The same method was applied to obtain the Jones matrix elements of a twisted nematic liquid crystal panel.