Hamiltonian formalism for general Lagrangian systems in an exceptional case

It is shown that in the exceptional case of a Lagrangian system, where the highest derivative of a generalized coordinate cannot be expressed in terms of the lower derivatives and the generalized momenta, the procedure to adopt in setting up the Hamiltonian formalism for the system (and consequently the quantization of the system) is to pass to an equivalent Lagrangian which does not have this defect and to use this rather than the original Lagrangian.