  Rio gave a concise bound for the central limit theorem in the Vaserstein
distances, which is a ratio between some higher moments and some powers of the
variance. As a corollary, it gives an estimate for the normal approximation of
the small jumps of the L\'evy processes, and Fournier applied that to the Euler
approximation of L\'evy-driven stochastic differential equations. However both
results are restricted to the one-dimensional case. It will be shown in this
article that, following Davie's idea, one can generalise Rio's result to
multidimensional case, and the number of moments required is independent of the
dimension. Also two different approaches are developed to simulate
multidimensional L\'evy SDEs: one as a corollary to the central limit bound,
the other directly derived from the L\'evy-Khinchine formula.
