The classical Hamiltonian for which the dynamics is represented by trajectories in a multidimensional phase (coset) space is quantized via Lyapunov analysis. A system of one electron in four sites and the vibration of H2O with Fermi resonance is studied. The quantization condition is that the average Lyapunov exponents show local minima as a function of the classical energy. This means that it requests the least global chaoticity. This quantization algorithm leads to results consistent with those obtained by the quantal models.