Let be a graph and . Then a subgraph of is called a -odd subgraph if for all . If for all , then a -odd subgraph is nothing but a matching. A -odd subgraph of is said to be maximum if has no -odd subgraph such that . We show that -odd subgraphs have some properties similar to those of matchings, in particular, we give a formula for the order of a maximum -odd subgraph, which is similar to that for the order of a maximum matching.