  A technique allowing for a perturbative treatment of nonlocal corrections to
the single-site dynamical mean-field theory (DMFT) in finite dimensions is
developed. It is based on the observation that in the case of strong electron
correlation the one-electron Green's function is strongly spatially damped so
that its intersite matrix elements may be considered as small perturbations.
Because the non-local corrections are at least quadratic in these matrix
elements, DMFT in such cases may be a very accurate approximation in dimensions
d = 1-3. This observation provides a rigorous justification for the application
of DMFT to physical systems. Furthermore, the technique allows for a systematic
evaluation of the nonlocal corrections. This is illustrated with the
calculation of the magnetic short range order parameter for nearest neighbor
spins in the half filled Hubbard model on the square lattice in its insulating
phase which exhibits an excellent agreement with the results of a recent
cluster approach.As a second example we study the lowest order correction to
the DMFT self-energy and its influence on the local density of states.
