The ro-vibrational interaction of tetratomic molecules is studied by using Lie algebra. It is the first time to give the formulae of non- diagonal matrix elements of tensor operators which can be employed to describe the ro-vibrational interaction for linear tetratomic molecules. As an example, the Z-doubling of ro-vibrational interaction of HCCF is computed by using these formulae.

Key words: ATOM, INTERACTIONS, tensor operator, reduced matrix element