A one-dimensional anisotropic photonic crystal is considered. A mathematical model is con-structed that separates an elliptical polarization wave into TE- and TM-type waves. The transformationmatrix is found for a periodic structure with an arbitrary number of layers in a period in the form of a blockdiagonal matrix. The transformation matrix is found for an arbitrary number of periods of the structure withanisotropic layers. Dispersion relations are found that determine the boundaries of the allowed zones.