A block-exact fast affine projection algorithm is described that is suitable for canceling long acoustic echoes. The algorithm has two advantages over conventional block algorithms: it has exactly the same convergence as its sample-by-sample version, achieved by compensation for errors from the sample-by-sample algorithm, and it has a flexible trade-off between complexity reduction and output delay, achieved by introducing two independent block lengths for filtering and updating. Comparison of the block-exact algorithm and with the fast affine projection algorithm under equal complexity conditions showed that the former has a faster convergence rate and a lower residual echo.