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This paper proposes an adaptive tap allocation technique based on the Kalman algorithm for minimizing the number of taps which are used for updating the equalizer coefficient. The conventional equalizer needs many taps to be adequate for the multipath channel with a long delay, which causes a high computational complexity for updating the coefficient. We propose a new method that the energy of tap and the channel delay length are observed during a training period and then the taps having negligible energy are gradually excluded from the coefficient update every channel delay length. The remaining taps form a new coefficient vector that reduces the computational complexity without any performance degradation. The proposed structure is simulated on the channel of the North American terrestrial high definition television (HDTV). Simulation results show that the computational complexity is almost 25 times lower than that of the conventional structure with the same convergence speed and mean square error (MSE) rate.