Discovery of binding sites is important in the study of protein-protein interactions. In this paper, we introduce stable and significant motif pairs to model protein-binding sites. The stability is the patterns resistance to some transformation. The significance is the unexpected frequency of occurrence of the pattern in a sequence dataset comprising known interacting protein pairs. Discovery of stable motif pairs is an iterative process, undergoing a chain of changing but converging patterns. Determining the starting point for such a chain is an interesting problem. We use a protein complex dataset extracted from the Protein Data Bank to help in identifying those starting points, so that the computational complexity of the problem is much released.