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For about two decades, numerous methods have been developed to blindly identify overdetermined (P≤N) mixtures of P statistically independent narrowband (NB) sources received by an array of N sensors. These methods exploit the information contained in the second-order (SO), the fourth-order (FO) or both the SO and FO statistics of the data. However, in practical situations, the probability of receiving more sources than sensors increases with the reception bandwidth and the use of blind identification (BI) methods able to process underdetermined mixtures of sources, for which P>N may be required. Although such methods have been developed over the past few years, they all present serious limitations in practical situations related to the radiocommunications context. For this reason, the purpose of this paper is to propose a new attractive BI method, exploiting the information contained in the FO data statistics only, that is able to process underdetermined mixtures of sources without the main limitations of the existing methods, provided that the sources have different trispectrum and nonzero kurtosis with the same sign. A new performance criterion that is able to quantify the identification quality of a given source and allowing the quantitative comparison of two BI methods for each source, is also proposed in the paper. Finally, an application of the proposed method is presented through the introduction of a powerful direction-finding method built from the blindly identified mixture matrix.