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This paper derives an adaptation algorithm named least mean modulus-Newton (LMM-Newton) algorithm that combines least mean modulus (LMM) algorithm with simple recurrent calculation of the inverse covariance matrix of the filter input using the Newton's method. The LMM-Newton algorithm achieves significant improvement in the convergence speed of complex-domain adaptive filters with a strongly correlated input. The algorithm is effective in making adaptive filter convergence as fast as that for the LMM algorithm with a white input process even in the presence of impulsive observation noise, preserving the robustness of the LMM algorithm against impulse noise. Through transient analysis and experiment with simulations and theoretical calculations of filter convergence, we demonstrate effectiveness of the LMM-Newton algorithm. Good agreement between simulated and theoretical convergence proves the validity of the analysis.