An analytical formula has been proposed to predict the high-lying spectral lines of rovibrational transitions for diatomic systems by Sun et al. who used multiple spectral difference method. This study improves the formula based on their previous work by adding a higher order spectral term Hv. Applications of this new formula to the AuO molecule shows that the accuracy of the P-branch rovibrational transition lines is about one order of magnitude better than the results obtained using the previous formula, and that the contributions of the small quantity Hv to the high-lying rovibrational energies and the transitional lines are shown to be important.