A modified indirect boundary element formulation is developed following a weighted residual approach. In this formulation, the fictitious source density, which appears in the integral equations of the method, is distributed on a surface which is exteriorly separated from the physical field boundary of the problem. The method does not require the evaluation of singular integrals and produces undeteriorated solutions at geometric discontinuities. The technique is applied to two-dimensional electromagnetic potential problems, and several examples are investigated.