Schwarz's iterative procedure of overlapping regions, which has been previously employed in the solution of polygonal waveguides and similar problems, is employed here to solve for the scattering matrix coefficients at the sharp junction of a sectoral and parallel-plate waveguides. It is shown that by dividing the junction into semi-infinite rectangular and sectoral subregions, and using the Green's functions of each, the problem is reduced to the solution of a system of integral equations of the Fredholm type. The scattering-matrix coefficients are computed and presented graphically as a function ofkb, together with the previously published data. The solution is relatively simple and the method is shown to be efficient since the fields are described in terms of rapidly convergent series (especially for a sectoral region of small flare angle), and accurate results are typically obtained after two or three iterations. It is shown that the method is applicable for sectoral regions of arbitrary flare angle, but a third circular subregion is particularly required for flare angles exceeding 180°.