Alternative simplified expressions have been deduced for f and g involved in the calculation of the true potential energy curves of such electronic states of diatomic molecules whose vibrational terms cannot be adequately represented by a quadratic in v + ½. These expressions have been used in calculating the true potential curve of the B 3 II 0u + state of 79 Br 81 Br molecule and the results show a close agreement with those obtained by Rees (1947). The true potential energy curve of the A 1 Σ+ state of LiH molecule has also been calculated by the present method and the results are found to agree quite well with those obtained by Fallon, Vanderslice and Mason (1960).