We have tested the new experimental techniques in the M\"ossbauer spectroscopy with Synchrotron M\"ossbauer Source by using the polarization analysis of the reflected radiation. In particular we have shown that the dichroic components in M\"ossbauer spectra create the scattering intensity with "rotated" polarization. The angular dependence for such component in the reflected signal is characterized by the peak near the critical angle of the total external reflection, and in the case of the collinear antiferromagnetic interlayer ordering the "magnetic" maxima on the reflectivity curve are formed mainly by this "rotated" polarization. The first experiment on M\"ossbauer reflectivity with selection of the "rotated" polarization shows the expected peak near the critical angle. The measured M\"ossbauer reflectivity spectra of the "rotated" polarization near the critical angle are rather different from the M\"ossbauer reflectivity spectra, measured without polarization analysis. They contain a smaller number of lines and can simplify the interpretation of the poorly resolved spectra. The enhanced surface sensitivity of the new technique is discussed.