Mesh is a widely used architecture in parallel computing systems. Research on efficient allocation of processors to incoming tasks on mesh architecture is very important in achieving the desired high performance. The processor allocation strategy proposed in this paper is based on a well-known boundary search approach and considers allocation time as a primary allocation decision-making factor. In this proposed technique, an additional novel heuristic is employed to consider, whenever feasible, having adjoining submeshes allocated to tasks with similar allocation times. The external fragmentation problem is expected to be alleviated, leading to improvement in utilization and shorter task waiting time. Another novel add-on feature is also employed to provide extra improvement. Our simulation results demonstrate substantial improvement in performance.