In this work, the performance of a tap selection based Minimum Mean Square Error (MMSE) equalization technique for high data rate Ultra Wideband (UWB) systems is evaluated for the first time using greedy method. This technique is shown to significantly outperform the conventional uniformly spaced equalizer with the same number of taps. In addition, the performance of strongest paths based tap selection method is compared with the greedy method. Larger performance gap is observed in the presence of Multiple Access Interference (MAI) and with increased SNR.