This paper presents a method for liquid crystal display characterization. It assumes a liquid crystal display can be considered as a polarization-changing device described by a Jones matrix plus a global phase. The Jones matrix parameters are found by a least squares minimization based on global optimization techniques. The present method avoids the need for assigning experimental values to theoretical expressions, and it is robust against intensity fluctuations, does not require arbitrarily fixing any sign of the parameters estimated, and only one quarterwave plate is employed. A comparative analysis of the results obtained with this method and previous ones is performed. Having completely characterized a liquid crystal display, a phase-mostly configuration is obtained and experimentally verified.Centro de Investigaciones Ópticas