The conditions under which a linear homogeneous anisotropic medium orthogonalizes polarization states of the input polarized light are studied. The criterion for orthogonalization in the form of inequality for the medium's parameters is obtained. The polarization orthogonalization properties of the some types of anisotropic medium have been investigated. The parameters, under which the orthogonalization occurs, and the states that are orthogonalized are found. All results obtained are illustrated using the Poincaré sphere representation.