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A procedure for accurate solution of scattering problems involving geometries with sharp edges by using physical optics-based characteristic basis functions, which themselves do not possess edge singularities, is presented in this communication. Our strategy is to employ special types of blocks that contain the free edges of the object, within which we can accurately represent the behaviors of the currents with rapidly varying amplitudes, still by using physical optics (PO)-types functions for the initial bases. The set of geometrical blocks which are associated solely with the edges extend along each edge, but have a relatively small width. The final number of characteristic basis functions using this approach is only slightly greater than that needed in the conventional characteristic basis function method (CBFM), which does not utilize the edge-block strategy. However, the accuracy in the final results is notably improved in some cases.