Abstract 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.