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An efficient method-of-moments (MoM) technique for analyzing non-periodic antenna arrays of identical elements with fixed orientation is presented. The proposed method, which uses macro basis functions (MBFs), is based on a compact representation of the interactions between MBFs. These interactions are expressed via a low-order harmonic-polynomial function after an explicit pre-computation of the reaction integrals in a very limited set of relative positions. This is possible for arrays of arbitrary size thanks to three transformations- subtraction of the far-field expression for the interactions, phase correction and modified radial distance- applied successively to the pre-computed interactions. After obtaining the harmonic-polynomial expressions, the computation time for the reaction integral between two MBFs is independent from the complexity of the antenna array element.