Energies of excitation of different electronic states of the oxygen molecule are calculated by the method of antisymmetrized molecular orbitals (ASMO). These are compared with the observed spectrum. It is found that the ASMO theory is most disappointing. The reasons for the failure of the method are analyzed. As a result of this critical analysis, a modified method is proposed which is found to be very successful. The basis of this modification is that the approximation of using atomic orbitals should be made only in evaluating the interaction energy of the constituent atoms of a molecule, and not to assess their isolated term values. As a corollary, the location of two new states of the oxygen molecule is predicted.