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A Fast Variable Step Size LMS (FVSSLMS-1) algorithm is proposed, which overcomes and avoids these drawbacks. In this algorithm, an appropriate time varying of the step size is calculated based on gradually decreasing maximum step size to the minimum value. This time varying step size is based on the square value of the current estimation error. A comparison between Least Mean Square (LMS), proposed, and another variable step size Normalized Least Mean Square (NLMS), adaptive algorithms are carried out. System identification was built and training using MATLAB simulation program as a form of software to test the right operation of adaptive system identification.