Let P be a set of n=2m+1 points in the plane in general position. We define the graph GMP whose vertex set is the set of all plane matchings on P with exactly m edges. Two vertices in GMP are connected if the two corresponding matchings have m−1 edges in common. In this work we show that GMP is connected and give an upper bound of O(n2) on its diameter. Moreover, we present a lower bound of n−2 and an upper bound of 2n−2 for the diameter of GMP for P in convex position.