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The modeling of the acoustic echo path was presented using multiple of small adaptive filters rather than using one long adaptive filter. A new approach is proposed using the concept of decomposing the long adaptive filter into low order multiple sub- filters in which the error signals are independent on each other. The independency of the error signals exhibits the parallelism technique. This achieves our goal in increasing speed of the convergence rate. Simulation results show that the proposed decomposed least-mean-square (LMS) adaptive algorithm significantly improved the convergence rate with respect to that of the original long adaptive filter. The proposed algorithm is also compared with multiple sub-filters approach used for acoustic echo cancellation as the technique of decomposition of error. This technique is based on using multiple sub-adaptive filters in which the error signals are dependent on each other. In this way the parallelism technique is not achieved and as the result the convergence rate increases. This is different from our proposed technique which is based on independency of the error signals to assure that our algorithm has faster convergence rate and minimum steady state error. The modeling of the acoustic echo path was represented by using three sub-adaptive filters of order =10 with fixed step size =0.05/3 for each adaptive filter. We use sinusoidal input signal with additive white gaussian noise (AWGN) for different signal-to-noise ratio to examine our approach.