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The relation between the method of moments (MoM) and high frequency techniques are discussed in view of the locality of the scattering phenomena. Firstly, locality in the high frequency diffraction is embodied in the MoM in view of the method of stationary phase. Local-domain basis functions accompanied with the phase detour, which are not entire domain but are much larger than the segment length in the usual MoM, are introduced to enhance the cancellation of the mutual coupling over the local-domain; the off-diagonal elements in resultant reaction matrix evanesce rapidly. Secondly, the Fresnel zone threshold is proposed for simple and effective truncation of the matrix into the sparse band matrix; the way mitigating computational load of the MoM in high frequency problems is suggested. The extended use of the Fresnel zone threshold in PO-MoM hybrid methods is also mentioned.