  In this work we propose a new numerical approach to distinguish between
regular and chaotic orbits in Hamiltonian systems, based on the simultaneous
integration of both the orbit and the deviation vectors using a symplectic
scheme, hereby called {\em global symplectic integrator}. In particular, the
proposed method allows us to recover the correct orbits character with very
large integration time steps, small energy losses and short CPU times. To
illustrate the numerical performances of the global symplectic integrator we
will apply it to two well-known and widely studied problems: the H\'enon-Heiles
model and the restricted three-body problem.
