Wedge is an important conanical structure in diffraction theory. Practically, a two-impedance wedge in a cold plasma may be used in modelling the electromagnetic scattering from a variety of large and complex object. The solution is corrected in comparison with that obtained for the problem in question by Bobrovnikov and Fisanov . In this study the scattered field is represented in the form of Sommerfeld integral with an unknown spectral function. By using the impedance boundary conditions a nonhomogeneous functional equation is obtained. The solution of the functional equation can be represented in terms of chi-functions and S integrals. After determining the unknown spectral function in the Sommerfeld integral, the Sommerfeld contour is deformed into the steepest descent paths. During the deformation process, the geometrical optic waves and the surface waves contributions are found. Diffraction coefficients is also discussed.