Based on the algebraic method (AM) presented in our previous study, a new algebraic approach (AM2) is suggested to evaluate accurate rovibrational energies and corresponding rotational constants using known experimental data of rovibrational energies of limited accuracy of a given rovibrational band for a diatomic electronic state. The results of reseach on rovibrational energies of the B1Σ electronic state of HF molecule shows that Algebraic Method 2 gives rovibrational energies in excellent agreement with experimental data, and the method generates reliable energies of high-lying rovibrational excited states which may be difficult to obtain experimentally or theoretically.