This paper describes the practical implementation and on the field test results of an Enhanced algorithm, based on Jones matrix Eigen analysis, to find the minimal polarization change points for the ALMA's line length corrector fiber stretcher. These points are complicated to find because they can be located at any point of the Poincare sphere and they also change after manipulation of fibers and with time, so the optimization of the fibers stretcher needs to be systematically checked and redone. The execution time of the original algorithm takes up to 20 minutes depending on the starting polarization state. This enhanced algorithm reduces this time in most of cases to less than a minute, with no intrinsic dependency on the starting point.