Data representation, matching algorithm and similarity measure are the main concern in protein structure matching. The above three points are considered in the implementation of Bipartite Graph Matching with Reference Frame algorithm (BGMRF). In BGMRF, the tertiary structures of protein Cα backbone are defined in reference frames representation. The matching vectors generated from the reference frames are integrated into bipartite graph as a representation to do the matching of structures. From bipartite graph, the problem is reduced to a network flow graph. The matching is solved using Ford-Fulkerson algorithm with Breadth First Search algorithm to find maximum weight matching. The experiment to identify Crambin-like family from dataset of small proteins shows that reference frames representation is well adapted to graph-based matching technique in BGMRF. For a dataset of 266 small proteins, BGMRF has successfully identified all 12 Crambin-like family members in the dataset.