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The sparse nature of a network echo response makes standard NLMS based adaptive algorithms perform poorly. Fast convergence, yet low complexity, of adaptive filter design causes another challenge. In this paper, a new Stochastic Selective Partial Update Normalized Least Mean Square (SSPNLMS) algorithm is proposed. Based on an efficient stochastic search and two block-based tap selection criteria, this algorithm exploits both sparseness of the echo response and sparseness of the input signal to achieve high quality adaptive filters without much computational cost. Simulation results show our proposed algorithm has promising convergence performance for the cases of white Gaussian noise input signal and the speech signals.