Experimental Mueller matrices contain certain amount of uncertainty in their elements and these uncertainties can create difficulties for decomposition methods based on analytic solutions. In an earlier paper [1], we proposed a decomposition method for depolarizing Mueller matrices by using certain symmetry conditions. However, because of the experimental error, that method creates over-determined systems with non-unique solutions. Here we propose to use least squares minimization approach in order to improve the accuracy of our results. In this method, we are taking into account the number of independent parameters of the corresponding symmetry and the rank constraints on the component matrices to decide on our fitting model. This approach is illustrated with experimental Mueller matrices that include material media with different Mueller symmetries. (C) 2016 Elsevier B.V. All rights reserved.