The accuracies of the predicted R-branch and Q-branch transitional lines of rovibrational diatomic systems for rotational states of J 100 are improved by using new analytical formulae and an improved difference converging method (DCM) in this study. The new formulae include the contributions from a higher-order energy term Hv. The improved DCM method includes a new physical converging criterion that is particularly useful in predicting unknown transitional lines. These improvements are used to study the transitional lines of the R-branch of the TiF and CO molecules and the Q-branch of the TiF molecule. The results show that the accuracies of the R-branch and Q-branch rotational lines are about one order of magnitude better than the results obtained using previous formulae; the new physical converging criterion can efficiently reduce the possible errors in the spectrum computations; the theoretical rotational lines obtained using the improved DCM method are much better than those obtained using the least-squares method.