Let G = (U, V, E) be an undirected bipartite graph. We specify some procedures that allow us to make efficiently the following 3-partition of the set E:E₁ is the set of edges belonging to all the maximum matchings (1-persistent edges); E₀ is the set of edges belonging to no maximum matching (0-persistent edges); E_w is the set of edges belonging to at least one maximum matching but not to all of them (weakly presistent edges).