We consider a particular type of similarity join: Given two sets of objects and a distance threshold r, find all the object pairs (one from each set) at distance at most r. For this sake, we devise a new metric index, coined List of Twin Clusters, which indexes both sets jointly (instead of the natural approach of indexing one or both sets independently). Our results show significant speedups over the basic quadratic-time naive alternative. Furthermore, we show that our technique can be easily extended to other similarity join variants, e.g., finding the k-closest pairs.