  The approach mapping from a matching of bipartite graphs to digraphs has been
successfully used for forcing set problem, in this paper, it is extended to
uniquely restricted matching problem. We show to determine a uniquely
restricted matching in a bipartite graph is equivalent to recognition a acyclic
digraph. Based on these results, it proves that determine the bipartite graphs
with all maximum matching are uniquely restricted is polynomial time. This
answers an open question of Levit and Mandrescu(Discrete Applied Mathematics
132(2004) 163-164).
