A new blind adaptive equalization method for constant modulus signals based on minimizing the approximate negentropy of the estimation error for a finite-length equalizer is presented. We consider the approximate negentropy using nonpolynomial expansions of the estimation error as a new performance criterion to improve the performance of a linear equalizer using the conventional constant modulus algorithm (CMA). Negentropy includes higher order statistical information and its minimization provides improved convergence, performance, and accuracy compared to traditional methods, such as the CMA, in terms of the bit error rate (BER). Also, the proposed equalizer shows faster convergence characteristics than the CMA equalizer and is more robust to nonlinear distortion than the CMA equalizer.