Computation of maximal matching of a graph based on Depth First Search tree computation was introduced by Datta and Sen (Parallel Algorithms and Applications,5, 1995, 161-164). They showed that the approach gives efficient parallel algorithms for maximal matching for graphs for which DFS tree can be efficiently computed. They also presented a parallel scheme to compute a maximal matching in O(T(n) log n) time using O(P(n)) number of processors, where T(n) and P(n) are the time and the number of processors required to compute DFS tree of a graph in parallel. We present here, an improved technique to compute maximal matching in parallel based on DFS tree computation. The algorithm takes O(T(n)) time and O(P(n)) processors.