We propose a new method for determining the Mueller matrix of an arbitrary optical element and verify it with three known optical elements. This method makes use of two universal SU(2) polarization gadgets to obtain the projection matrix directly from the experiment. It allows us to determine the Mueller matrix without precalibration of the setup, since the generated polarization states are fully determined by the azimuths of the wave plates. We calculate errors in determining the Mueller matrix and compare with other techniques. © 2014 Optical Society of America.