Fragmentation is the main performance bottleneck of large, multi-user multicomputer system. This paper presents an L-Shaped Submesh Allocation(LSSA) strategy, which lifts the restriction on the rectangular shape formed by allocated processors in order to address the problem of fragmentation. LSSA can manipulate the shape of the required submesh to fit into the fragmented mesh system. Thus, LSSA accommodates incoming jobs faster than other strategies and results in the reduction of job response time. Extensive simulations show that LSSA performs more efficiently than other strategies in terms of the external fragmentation, the job response time and the system utilization.