The use of models of fictitious elemental current sources, located inside the scatterer to simulate the scattered field, has proved to be an efficient computational technique for analyzing scattering by metallic bodies. This paper presents a novel modification of the technique in which the omnidirectional elemental sources are arranged in groups of array sources with directional radiation patterns, and the boundary testing points are arranged in groups of testing arrays with directional receiving patterns. This modification which is motivated by physical understanding is equivalent to mathematical basis transformations. It renders the system matrix more localized and thereby enables the analysis of larger bodies. The new approach is applied to the case of TM scattering by a perfectly conducting square cylinder with side-length of 20λ. Reduction of 50% in the number of the nonzero elements of the system matrix is achieved with virtually no degradation in the accuracy of the radar cross section (RCS) calculations.