A simple partial Mueller polarimeter is described, consisting of two linear polarizers and two liquid crystal variable retarders. The measurement leads to an incomplete Mueller-Scierski matrix, in which the elements from the third row and the third column are simultaneously missing. The proposed procedure for determining information about the birefringent medium from such an incomplete matrix is based on numerical methods and carrying out measurements with the rotated azimuthal sample. Acquired from the obtained results, the missing elements of the Mueller-Scierski matrix are reconstructed. The correctness of the method was verified by numerical simulations and test measurements.