Using expansion formulas for the Slater-type orbitals (STOs) obtained by the one of authors [Phys. Rev. A 31 (1985) 2851] the two-center overlap integrals with different screening parameters are expressed through the overlap integrals with the same screening parameter. The series representation of overlap integrals obtained in this paper is useful for small differences of the exponential parameters. For large differences of the exponential parameters the convergence of the infinite series becomes rather slow. (C) 2001 Elsevier Science B.V. All rights reserved.