The lowest 3Σu+ and 1Σu+ states of the hydrogen molecule, the interaction energy between two normal helium atoms and the 3B1u and 1B1u states of the ethylene molecule are treated by the method of the molecular orbitals in the single configuration approximation. The results are encouraging and the reason for this success is that we have used molecular orbitals which are a little more flexible than the conventional LCAO MO's. It is confirmed that the failue of the conventional ASMO LCAO approximation does not necessarily imply the break-down of the useful concept of “molecular orbital” itself.