A matrix Wiener-Hopf equation connected with a new canonical diffraction problem is solved explicitly. We consider the diffraction of a plane electromagnetic wave by an impedance loaded parallel plate waveguide formed by a two-part impedance plane and a parallel perfectly conducting half-plane. The representation of the solution to the boundary-value problem in terms of Fourier integrals leads to a matrix Wiener-Hopf equation. The exact solution is obtained in terms of two infinite sets of unknown coefficients satisfying two infinite systems of linear algebraic equations. These systems are solved numerically and the influence of the parameters such as the waveguide spacing and the surface impedances of the two-part plane on the diffraction phenomenon is shown graphically. Copyright (c) 2005 John Wiley & Sons, Ltd.