It is common practice to apply linear or nonlinear feature extraction methods before classification. Usually linear methods are faster and simpler than nonlinear ones but an idea successfully employed in the nonlinearization of Support Vector Machines permits a simple and effective extension of several statistical methods to their nonlinear counterparts. In this paper we follow this general nonlinearization approach in the context of Independent Component Analysis, which is a general purpose statistical method for blind source separation and feature extraction. In addition, nonlinearized formulae are furnished along with an illustration of the usefulness of the proposed method as an unsupervised feature extractor for the classification of Hungarian phonemes.