Datasets obtained by large-scale, high-throughput methods for detecting protein-protein interactions typically suffer from a relatively high level of noise. We describe a novel method for improving the quality of these datasets by predicting missed protein-protein interactions, using only the topology of the protein interaction network observed by the large-scale experiment. The central idea of the method is to search the protein interaction network for defective cliques (nearly complete complexes of pairwise interacting proteins), and predict the interactions that complete them. We formulate an algorithm for applying this method to large-scale networks, and show that in practice it is efficient and has good predictive performance. More information can be found on our website http://topnet.gersteinlab.org/clique/