  We introduce a new methodology for a fast and reliable discrimination between
ordered and chaotic orbits in multidimensional Hamiltonian systems which we
call the Linear Dependence Index (LDI). The new method is based on the recently
introduced theory of the Generalized Alignment Indices (GALI). LDI takes
advantage of the linear dependence (or independence) of deviation vectors of a
given orbit, using the method of Singular Value Decomposition at every time
step of the integration. We show that the LDI produces estimates which
numerically coincide with those of the GALI method for the same number of $m$
deviation vectors, while its main advantage is that it requires considerable
less CPU time than GALI especially in Hamiltonian systems of many degrees of
freedom
