Using Talman's formulae for overlap integrals in lined-up coordinate systems and Guseinovs transformation technique, a new algorithm is presented for computing the two-center overlap integrals over Slater type orbitals (STOs) with respect to the molecular coordinate system (nonlined-up coordinate systems) appearing in the Hartree-Fock-Roothaan (HFR) equations. The numerical stability of the computational results is analyzed.