In this paper we propose an alternative statistical Gaussianity measure whose optimization provides the extraction of one non-gaussian independent component at each stage of an ICA procedure; this measure is based on the Cumulative Density Function (cdf) instead of traditional distribution distances over Probability Density Functions (pdf’s). Additionally, a novel multistage-deflation algorithm is proposed in order to perform ICA in multidimensional scenarios very efficiently; although this approach can be applied to any multistage ICA method, we have developed it to speed up our ICA procedure based on Order Statistics (OS). The algorithm consists on a gradient learning rule plus an orthonormalization projection technique that decreases the vector space dimension progressively ¹.