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A method for decomposing an asymmetrical structure into two substructures is given. One substructure contains the attributes of symmetry while the remainder or residual substructure contains the attributes of asymmetry. The decomposition is constructed such that the superposition of the radiated electromagnetic fields of the decomposition substructures gives the radiated fields of the original structure. Although the decomposition substructures can, by superposition, be used to compute the total radiated fields of the original structure, this is not the primary purpose of the decomposition. The primary importance of the decomposition technique is to provide insight into methods for reducing the emissions of each substructure and consequently those of the original structure. In many cases the emissions of the asymmetric substructure are the dominant contributors to the total emissions of the original structure. In this case, the decomposition substructures allow direct insight into the reduction of the total emissions that was previously available only for the symmetric substructure.