The wavelet transform domain least mean square (WTLMS) is knew to have, in general, a fast convergence rate than the LMS algorithm. Through analysing the redundancy existed in the WTLMS algorithm, how to remove structural redundancy is showed, which in turn reduces the computational load of the algorithm. The method of how to transform the non-causal system into causal system is also given. The simulation results show that the proposed algorithm also could be used to identify the parameters of the IIR filters, and it also show that the improving WTLMS have the higher speed than the WTLMS algorithm .