Wedge is an important canonical structure in diffraction theory, a two-impedance wedge in a cold plasma may practically be used in modeling the electromagnetic scattering from a variety of large and complex objects. In this study, the scattered field is represented in the form of a 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 is represented in terms of χ-functions and S integrals. After determining the unknown spectral function in the Sommerfeld integral, the Sommerfeld contour is deformed into the steepest descent path to derive the expression of the diffraction coefficients.