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Two formulations have been used so far in quantum mechanical studies of the rotation-vibration of non-linear triatomic molecules: the first formulation uses the rotation-vibration Hamiltonian for polyatomic molecules established by Darling and $Dennison1$ according to a method proposed by Wilson and $Howard2$; the second formulation makes use of the Hamiltonian for the three-body problem as proposed by H. Diehl, S. Flugge, U. Schr""{o}der. A. V""{o}lkel and A. $Weiguny.2$ We have written down, for the rotation-vibration of non-linear triatomic molecules, a general Hamiltonian which holds for an arbitrary choice of both the set of internal coordinates and the molecule-fixed rotating framework. This general Hamiltonian includes as special cases the two formulations described above and it allows a better understanding of the relations existing between them. These relations will be discussed.