We describe a new setup for a snapshot Mueller matrix polarimeter (SMMP). It relies on the separation and orthogonal polarization of two light beams by a Wollaston prism located at the setup output. The simultaneous treatment of the two spectra allows an enhancement of accuracy for real-time measurements through reduction of the effects caused by random noise and systematic errors. Moreover, it gives insight into the nonuniform spectral response of the medium under study. Experimental results support the feasibility of the proposed technique.