This article presents a variation of the integral transform method to evaluate multicenter bielectronic integrals (12͉34), with 1s Slater-type orbitals. It is proved that it is possible to define, out of the expression of (12͉34) given by the integral transform method, a function F(q) that has the property of having a unique Q, such that F(Q) ϭ (12͉34). Therefore, F(q) may be used to calculate (12͉34). It is shown that the evaluation of F(Q) turns out to be simpler than the three-dimensional integral involved in the calculation of (12͉34), and an algorithm is presented to calculate Q. The results show that relative errors on the order of 10 Ϫ3 or lower are obtained very efficiently. In addition, it is shown that the proposed algorithm is very stable.