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In this paper we consider the scattering by a thick impedance half plane in the situation of a normally incident plane wave. The solution is based on the angular spectrum method in connection with the generalized scattering matrix formulation (GSMF) and as such it closely follows a parallel formulation applied recently in the diffraction analysis of the perfectly conducting thick half plane. Essentially, the angular spectrum method is first used to obtain the diffraction, coupling, reflection and radiation (or launching) coefficients relating to a pair of thin parallel impedance half planes which are then employed in the GSMF. The coefficients follow after an approximate solution of the resulting coupled dual integral equations which are derived in terms of the electric and magnetic current spectra. Several backscatter patterns are presented and compared with corresponding patterns based on the geometrical theory of diffraction (GTD) and a numerical model. It is found that a combination of the simple GTD solution and the present results give an acceptable solution for the diffraction by impedance half planes of almost any thickness.