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Proposed is a normalised subband adaptive filter algorithm with a variable step size based on the mean-square deviation (MSD) analysis. Since the spectrum of each input signal in subbands is close to that of white noise, the MSD can be approximated. The step size in this study is chosen such that the MSD undergoes the largest decrease from one iteration to the next, which leads to a fast convergence rate and a small misalignment. Simulation results confirm that the proposed algorithm outperforms existing algorithms in the literature.