Abstract: Through the introduction of dynamical symmetry, the method of construct the Hamiltonian of the molecule is derived and the general method of dealing with ＂vibration-vibration coupling＂ and ＂vibration-rotation coupling＂ molecular spectroscopy are deduced. An example （HCO molecule） is induced to elucidate this method by choosing a certain group chain to construct Hamiltonian of this molecular system and illustrating that the group chain is unique. It also makes a principal introduction of some other applications of Lie algebra method in the molecular spectroscopy （e. g. local-mode, the spectroscopy＇of multi-atomic molecule） and elucidates some question of this method in the last of this paper.

Key words: symmetry, Lie algebra, group chain, uniqueness