In this paper, we introduce a procedure for separating a multivariate distribution into nearly independent components based on minimizing a criterion defined in terms of the Kullback-Leibner distance. By replacing the unknown density with a kernel estimate, we derive useful forms of this criterion when only a sample from that distribution is available. We also compute the gradient and Hessian of our criteria for use in an iterative minimization. Setting this gradient to zero yields a set of separating functions similar to the ones considered in the source separation problem, except that here, these functions are adapted to the observed data. Finally, some simulations are given, illustrating the good performance of the method.