We investigate the problem of fi nding optimal one-bit perturbation that maximizes the size of the basin of attractions (BOAs) of desired attractors and minimizes the size of the BOAs of undesired attractors for large-scale Boolean networks by cascading aggregation. First, via the aggregation, a necessary and sufficient condition is given to ensure the invariance of desired attractors after one-bit perturbation. Second, an algorithm is proposed to identify whether the one-bit perturbation will cause the emergence of new attractors or not. Next, the change of the size of BOAs after one-bit perturbation is provided in an algorithm. Finally, the efficiency of the proposed method is verifi ed by a T-cell receptor network.