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This paper proposes a new low-complexity transform-domain (TD) adaptive algorithm for acoustic echo cancellation. The algorithm is based on decomposing the long adaptive filter into smaller subfilters and employing the selective coefficient update (SCU) approach in each subfilter to reduce computational complexity. The resulting algorithm combines the fast converging characteristic of the TD decomposition technique and the benefits of the SCU of low complexity with minimal performance losses. The improvement in convergence speed comes at the expense of a corresponding increase in misadjustment. To overcome this problem, a hybrid of the proposed algorithm and the standard TD LMS algorithm (TDLMS) is presented. The hybrid algorithm retains the fast convergence speed capabilities of the original algorithm while allowing for low final MSE. Simulations show that the hybrid algorithm offers a superior performance when compared to the standard TDLMS algorithm with less computational overhead.