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A contrast function for independent component analysis (ICA) is presented incorporating the prior knowledge on the sub-Gaussian or super-Gaussian character of the sources as described by their kurtosis signs. The contrast is related to the maximum likelihood principle, reduces the permutation indeterminacy typical of ICA, and proves particularly useful in the direct extraction of a source signal with distinct kurtosis sign. In addition, its numerical maximization can be performed cost-effectively by a Jacobi-like pairwise iteration. Extensions to standardized cumulants of orders other than four are also given.