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Introduction) DV-Xa method uses numerical basis functions adaptable for the circumstance in a molecule. But they are calculated based on spherically symmetric potential for each atom. Newly proposed method inherits DV-Xa-s merit but isn-t restricted by the premise of atomic spherical symmetry. Aim of the study) This method is being developed as a powerful tool to calculate MOs under complicated outer potential, especially vector potential. Method) Basis functions are calculated by operations of matrices representing physical quantities and vectors representing wave functions. Analytical assists, like spherical harmonic functions, are not necessary at all. Hartree-Fock-Slater equations for molecules can be expressed numerically even for arbitrary outer potential and solved easily as eigenvalue problems of matrix. But basis functions for an atom are defined only on sample points proper to that atom. On the other hand, basis functions need to be defined on all sample points to calculate Fock matrices for LCAO-MO calculation. The author will explain some techniques to pass over this gap at this presentation. Results) LCAO-MO calculations were tested within real wave functions. Total energy vs interatomic-distance curves for N2, F2 and CO were calculated and showed minima near experimental equilibrium distances. Dipole moments of CO, O3 and NH3 were calculated and matched semi-quantitatively experimental moments. Calculations of basis functions were heavy but showed O(n) dependence. Conclusion) It was demonstrated that basis functions calculated by matrix operation can be used well for LACO-MO calculation. When wave functions are extended to complex, this method will serve as a useful tool to treat MOs under complicated magnetic fields.