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For greatly overcoming disadvantages of low convergent rate and high mean square error of constant modulus algorithm (CMA) and defects of high computational complexity of polyspectra algorithms, sign kurtosis maximization adaptive algorithm (SKM-AA) for updating blind equalizer weight vectors is developed based on kurtosis of stochastic signals, the stochastic ascend approach, and sign algorithm. In this algorithm, the sign of the equalizer output signal function is extracted and used as the updating factor of equalizer weight vectors to decrease the computational load of updating blind equalizer weight vectors. Accordingly, performance of the SKMAA in convergent speed and residual mean square error (MSE) is much better than that of CMA. The efficiency of SKMAA is proved via computer simulation of the underwater acoustic channel (UWAC) equalization.