In the determination of the energy levels and wavefunctions of the highly excited ro-vibrational states for the triatomic molecules, it is important to use the suitable coordinates for computational simplicity. For example, Jaccobi coordinates are often used for the floppy and van der Waals triatomic molecules, whereas the bondlength-bondangle coordinates or Radau coordinates are usually used for the stable triatomic molecules. In this note, a generalized ro-vibrational Hamiltonian for the triatomic molecules is presented.From this Hamiltonian, one can conveniently write down the explicit expression of the ro-vibrational Hamiltonian in the coordinates which are actually used. For example, Jaccobi coordinates are often used for the floppy and van der Waals triatomic molecules, whereas the bondlength-bondangle coordinates or Radau coordinates are usually used for the stable triatomic molecules. In this note, a generalized ro-vibrational Hamiltonian for the triatomic molecules is presented. Let this Hamiltonian, one can conveniently write down the explicit expression of the ro-vibration Hamiltonian in the coordinates which are actually used.