Combining multiple clusterings arises in various important data mining scenarios. However, finding a consensus clustering from multiple clusterings is a challenging task because there is no explicit correspondence between the classes from different clusterings. We present a new framework based on soft correspondence to directly address the correspondence problem in combining multiple clusterings. Under this framework, we propose a novel algorithm that iteratively computes the consensus clustering and correspondence matrices using multiplicative updating rules. This algorithm provides a final consensus clustering as well as correspondence matrices that gives intuitive interpretation of the relations between the consensus clustering and each clustering from clustering ensembles. Extensive experimental evaluations also demonstrate the effectiveness and potential of this framework as well as the algorithm for discovering a consensus clustering from multiple clusterings.