The procedure proposed by F. A. Sikta et al (IEEE Trans. Ant. Prop. , vol. AP-31, pp. 584-585, July 1983) is easily and efficiently improved by conveniently utilizing the uniform geometrical theory (UTD) solution for double diffraction in the far zone of a plane wave. It is shown that the same equivalent-current concept can be applied to treat the case of plates with a dielectric coating, which are approximately represented by a surface-impedance boundary condition. To this end, the solution given by G. D. Maliuzhinets (1958), for the diffraction at the edge of a wedge with two different surface-impedance faces, is suitable to define first-order equivalent currents at the edges of each strip.