We propose a new algorithm for the rapid evaluation of electron repulsion integrals over Gaussian type orbitals, termed elementary basis algorithm (EBA). In the EBA, the information of the atomic basis functions is divided into two parts: an elementary and an atomic basis part. In the conventional algorithm, all information is assigned to atoms, which requires that all computations must be performed in the atomic loops. In the EBA, computations can be partly carried out in the elementary loops. We apply the EBA to the accompanying coordinate expansion method of Ishida. (C) 2004 Elsevier B.V. All rights reserved.