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This paper introduces a new variable step-size LMS algorithm in which the step-size is dependent on both data and error normalization. With an appropriate choice of the value of the fixed step-size and the ratio between error and data normalization in the proposed algorithm, a trade-off between speed of convergence and misadjustment can be achieved. The performance of the algorithm is compared with other LMS-based algorithms in several input environments. Computer simulation results demonstrate substantial improvements in the speed of convergence of the proposed algorithm in a stationary environment over other algorithms with the same small level of misadjustment. In addition, the proposed algorithm shows superior tracking capability when the system is subjected to an abrupt disturbance. For a nonstationary environment, the performance of the algorithm is equivalent to other time-varying step-size algorithms.