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The so-called "super-exponential" methods (SEMs) are attractive methods for solving blind signal processing problems. The conventional SEMs, however, have such a drawback that they are very sensitive to Gaussian noise. To overcome this drawback, we propose a new SEM. While the conventional SEMs use the second- and higher order cumulants of observations, the proposed SEM uses only the higher order cumulants of observations. Since higher order cumulants are insensitive to Gaussian noise, the proposed SEM is robust to Gaussian noise, which is referred to as a robust super-exponential method (RSEM). To show the validity of the proposed RSEM, some simulation results are presented.