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In this paper,we propose an approach to nucleon-pair approximation (NPA) with m-scheme bases,in which the collective nucleon pairs are represented in terms of antisymmetric matrices,and commutations between nucleon pairs are given using a matrix multiplication that avoids angular-momentum couplings and recouplings.Therefore the present approach significantly simplifies the NPA computation.Furthermore,it is formulated on the same footing with and without isospin.