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In acoustic echo cancellation (AEC) systems, the partitioned block frequency-domain adaptive filter (PBFDAF) algorithm is commonly adopted to improve the computational efficiency and convergence rate. However, the PBFDAF algorithm introduces an inherent delay. Delayless PBFDAF algorithms have been proposed to tackle this issue. However, the complexity of the existing delayless PBFDAF algorithms is high. Some have high average complexity, but others have high peak complexity. A computationally efficient delayless PBFDAF algorithm is proposed in this letter to reduce both the average and peak complexity. Moreover, a delay compensation method is presented to compensate the error path delay and thus speed up the convergence rate. Simulation results demonstrate that the convergence and tracking performance of the new algorithm with delay compensation is comparable with that of the PBFDAF algorithm.