This paper proposes an innovative Pipeline-based Maximal-sized Matching scheduling approach, called PMM, for input-buffered switches. It dramatically relaxes the timing constraint for arbitration with a maximal matching scheme. In the PMM approach, arbitration operates in a pipelined manner, where K subschedulers are used. Each subscheduler is allowed to take more than one time slot for its matching. Every time slot, one of them provides the matching result. The subscheduler can adopt a pre-existing efficient maximal matching algorithm such as iSLIP and DRRM. PMM maximizes the efficiency of the adopted arbitration scheme by allowing sufficient time for a number of iterations. We show that PMM preserves 100% throughput under uniform traffic and fairness for best-effort traffic of the pre-existing algorithm.