In the present work, the scattering of a wave radiating inside a waveguide consisting of two coaxial cylinders the inner of which is infinite and has piecewise surface impedance, while the outer cylinder is infinitely thin, semi-infinite and perfect electrical conductor is analyzed using Wiener-Hopf technique. The problem is defined as a Wiener-Hopf equation by applying Fourier transformation to the scattered field and the boundary conditions. The scattered field inside the waveguide is expanded to series in terms of waveguide modes and the solution is obtained using the continuity conditions for the electromagnetic fields and transforming the problem into three sets of infinite algebraic equations containing three sets of infinite constants. In the numerical results section, the effects of the geometrical parameters and the impedances of the waveguide to the radiated field and the reflection coefficient is observed. Obtained results are compared to a previously solved problem.