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This paper derives a new adaptation algorithm named recursive least moduli (RLM) algorithm that combines least mean modulus (LMM) algorithm for complex-domain adaptive filters with recursive estimation of the inverse covariance matrix of the filter reference input. The RLM algorithm achieves significant improvement in the filter convergence speed of the LMM algorithm with a strongly correlated filter reference input, while it preserves robustness of the LMM algorithm against impulsive observation noise. Analysis of the RLM algorithm is developed for calculating transient and steady-state behavior of the filter convergence. Through experiment with simulations and theoretical calculations of the filter convergence for the RLM algorithm, we demonstrate its effectiveness in making adaptive filters fast convergent and robust in the presence of impulse noise. Good agreement between the simulations and theory proves the validity of the analysis.