In this article we consider the electronic diabatic presentation of a two-state system with the aim of earning insight regarding the distribution of conical intersections in a given region. In this process we revealed explicit relationship between the diabatic potentials and the locations of conical intersections. The study is accompanied with numerical examples as worked out for a model and ab initio potential energy surfaces of the Na+H-2 system. (C) 2004 American Institute of Physics.