Diffraction by a two-part plane is an important topic in diffraction theory, and is relevant for many applications. Although various examples have been treated by several authors as contributions to this class of problems, a common characteristic of all these problems is that they were discontinuous only in one direction of the surface. The generalization of this type of a problem is to have an anisotropic boundary condition on each half-plane. Here we consider such a configuration where the half planes are conducting in one direction and having different impedances in the other direction. This boundary-value problem is formulated by Fourier transform technique which leads to a scalar Wiener-Hopf equation and is solved by standard techniques. Then asymptotic expressions for the diffracted fields are obtained by evaluating the field integrals asymptotically. These expressions reduce to the known results related to the reflection mechanisms only when Z1 = Z2 which correspond to the situation of full impedance plane.