Co-Simrank is a useful Simrank-like measure of similarity based on graph structure. The existing method iteratively computes each pair of Co-Simrank score from a dot product of two Pagerank vectors, entailing O(log(1/e)n3) time to compute all pairs of Co-Simranks in a graph with n nodes, to attain a desired accuracy e. In this study, we devise a model, Co-Simmate, to speed up the retrieval of all pairs of Co-Simranks to O(log2(log(1/e))n3) time. Moreover, we show the optimality of Co-Simmate among other hop-(uk) variations, and integrate it with a matrix decomposition based method on singular graphs to attain higher efficiency. The viable experiments verify the superiority of Co-Simmate to others.