The asymptotic expressions for the total field excited by a plane wave obliquely incident on a wedge with anisotropic impedance faces are represented in the framework of the uniform geometrical theory of diffraction. The problem of decoupling the functional difference equations is solved by applying the perturbation technique on the basis of two analytical solutions: normal incidence and grazing to the edge incidence. The numerical results agree well with those presented in published papers and provide a uniform and continuous behavior of the field dependent upon the skewness of the incident wave outside the wedge region.