Mulliken's method for obtaining gross atom-charges has been modified by use of a partitioning of the overlap densities which preserves their dipole moment. The gross atom charges are now determined by the elements of (P両), rather than (PS), where 両 is a non-symmetric matrix whose elements depend upon the various overlap integrals, internuclear distances, and centroids of the overlap densities. The method is applied to the ground-states of some first-row diatomic molecules. For comparison, contours of the one-electron density function, and a difference density function, are presented for BH and FH. The effective atomic charges and contour diagrams are both calculated by use of two different sets of atomic basis functions. The calculated effective atomic charges are sensitive to both the choice of basis functions and the method used for partitioning the overlap densities.