An improved partial Haar transform （PHT） algorithm is proposed in this paper to improve the convergence of the first filter W₁（k） in the dual filter structure （DFS）. In the new algorithm， the W₁（k） adapts using a PHT version of the input signal to decrease its length. The convergence of W₁（k） is further improved by optimizing the step size to minimize the a posteriori error. Finally， the normalized factor of the algorithm is calculated and maintained piecewisely to save computation. By increasing the convergence of the W₁（k）， the proposed algorithm requires less adaptations to achieve a delay estimation of the adaptive system， and the overall convergence of the DFS is eventually improved with the proposed algorithm. The simulation results in the context of echo cancellation indicate that compared with other traditional adaptive algorithms， the proposed algorithm is found to be more efficient in sparse system identification.