The diffraction by a resistive sheet attached to a two-sided impedance plane, made up by perfectly electric conducting and impedance half-planes, is presented. AnE-plane wave normally illuminates this structure, therefore, the problem is a two dimensional one. By using Sommerfeld-Maliuzhinets' method, the problem is reduced to the solution of a coupled system of functional equations for two spectral functions corresponding to the two spatial regions defined by the resistive sheet. By eliminating either of the spectral functions, a second-order difference equation with variable 2π-periodic coefficients is obtained for the remaining one. A general method of constructing a single-valued solution of this second-order difference equation is presented based on the Fourier transform. It is shown that the obtained single-valued meromorphic spectral function satisfies the edge condition, pole requirement and the radiation condition.