In this paper, we present a new method that speeds up the convergence of the infomax algorithm proposed by Bell and Sejnowski. One effect of the infomax algorithm is that the 2nd order and 4th order statistical correlations are reintroduced to the signals during the learning process due to the optimization with respect to the complete signal statistics. We show that repetitively forcing 2nd and 4th order correlations to zero speeds up the convergence and improves separating sources with fewer data points.