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The objective of the beamforming with the exploitation of a sensor array is to enhance the signals of the sources from desired directions, suppress the noises and the interfering signals from other directions, and/or simultaneously provide the localization of the associated sources. In this paper, we present a higher order cumulant-based beamforming algorithm, namely, the super-exponential blind adaptive beamforming algorithm, which is extended from the super-exponential algorithm (SEA) and the inverse filter criteria (IFC). While both SEA and IFC assume noise-free conditions, this requirement is no longer needed, and all the noise components are taken into account in the proposed algorithm. Two special conditions are derived under which the proposed blind beamforming algorithm achieves the performance of the corresponding optimal nonblind beamformer in the sense of minimum mean square error (MMSE). Simulation results show that the proposed algorithm is effective and robust to diverse initial weight vectors; its performance with the use of the fourth-order cumulants is close to that of the nonblind optimal MMSE beamformer.