  We provide a Lyapunov type bound in the multivariate central limit theorem
for sums of independent, but not necessarily identically distributed random
vectors. The error in the normal approximation is estimated for certain classes
of sets, which include the class of measurable convex sets. The error bound is
stated with explicit constants. The result is proved by means of Stein's
method. In addition, we improve the constant in the bound of the Gaussian
perimeter of convex sets.
