A non-empirical valence-electron method suitable for molecular orbital calculations on large molecules containing heavy atoms is described. The method uses a minimum STO basis for the valence orbitals and accounts for core-valence interactions by means of a simple pseudopotential which affords corrections to the diagonal F matrix elements. All integrals involving one and two centres are included, and these are evaluated theoretically. The method produces electronic energies and electron density properties which are comparable with those of corresponding all-electron ab-initio calculations. In this paper two versions of the method are described, the basic non-parametric method and the parametric method which involves a simple modification for the two-centre integrals involving atoms of different size or electronegativity. Results of calculations on first-row diatomic molecules are described. It is hoped that the method will be suitable for calculations on larger molecules and molecules containing heavier atoms.