  Understanding the dynamics of multi--dimensional conservative dynamical
systems (Hamiltonian flows or symplectic maps) is a fundamental issue of
non-linear science. The Generalized ALignment Index (GALI), which was recently
introduced and applied successfully for the distinction between regular and
chaotic motion in Hamiltonian systems \cite{sk:6}, is an ideal tool for this
purpose. In the present paper we make a first step towards the dynamical study
of multi--dimensional maps, by obtaining some interesting results for a
4--dimensional (4D) symplectic map consisting of N=2 coupled standard maps
\cite{Kan:1}. In particular, using the new GALI$_3$ and GALI$_4$ indices, we
compute the percentages of regular and chaotic motion of the map equally
reliably but much faster than previously used indices, like GALI$_2$ (known in
the literature as SALI).
