We note that non-direct product bases are also used in vibrational dynamics. These generally come from partitioning the full Hamiltonian into two sub-Hamiltonian in nonoverlaping modes plus an interaction part. Diagonalization of the sub-Hamiltonians yields a new basis in the corresponding modes, which can then be used in new direct-product representation. Matrix elements in this new basis are then done and a final H-matrix is obtained.