In this work, a new modified LMS algorithm to adjust thecoefficients of an adaptive digital filter is presented. Starting from the basic LMS (Least Mean Square) algorithm, the modified algorithm LMSm has been conceived as to achieve-for a determined number of iterations borh properties in parallel: a faster convergence rate and a smaller final quadratic error then the LMS and nLMS algorithms. The underlaying idea was its application to digital communication channel identification and later equalization which requires a high frequency of operation. These properties have been analytically derived and its behavior has extensively been verified. Both, analytical and experimental results obtained by using the LMSm algorithm in standard digital channel models, show the following important improvements: a higher velocity of convergence and a smaller mean squared error between the model identified by the system. and the real channel parameters