Given a universe of local communities of a large network, we aim at identifying the meaningful and consistent communities in it. We address this from a new perspective as the process of obtaining consensual community detections and formalize it as a bi-clustering problem. We obtain the global community structure of the given network without running expensive global community detection algorithms. The proposed mathematical characterization of the consensus problem and a new biclustering algorithm to solve it render the problem tractable for large networks. The approach is successfully validated in experiments with synthetic and large real-world networks, outperforming other state-ofthe-art alternatives in terms of speed and results quality.