Efficient utilization of processing resources in a large multicomputer system with the possibility of fault occurrence depends on the reliable processor management scheme. This paper presents a dynamic and reliable processor allocation strategy to increase the performance of mesh-connected parallel systems with faulty processors The basic idea is to reconfigure a faulty mesh system into a maximum convex system using the fault-free upper or lower boundary nodes to compensate for the non-boundary faulty nodes. To utilize the non-rectangular shaped system parts, our strategy tries to allocate L-shaped submeshes instead of signaling the allocation failure. Extensive simulations show that the strategy performs more efficiently than other strategies in terms of the job response time md the system utilization.