A general view of the backscattering Mueller matrix for the quasi-horizontally oriented hexagonal ice crystals of cirrus clouds has been obtained in the case of tilted and scanning lidars. It is shown that the main properties of this matrix are caused by contributions from two qualitatively different components referred to the specular and corner-reflection terms. The numerical calculation of the matrix is worked out in the physical optics approximation. These matrices calculated for two wavelengths and two tilt angles (initial and present) of CALIPSO lidar are presented as a data bank. The depolarization and color ratios for these data have been obtained and discussed.