The efficient allocation problem plays an important role in partitionable multiprocessor system. It is critical to the performance of parallel computers, especially for large-scale parallel computers. In this paper, we propose a new enhanced two-dimensional buddy system (E2DBS) strategy which overcomes the drawbacks of previous two-dimensional buddy system (2DBS) strategy, such as four non-buddy submeshes can be allocated, the requesting tasks and the system needs not be square. In E2DBS, we propose an adaptive data structure, called free sub-mesh matrix (FSM), to maintain the free submeshes, which can allocate and deallocate processors easily. Simulation results indicate that our strategy outperforms the previous ones, i.e. 2DBS strategy and best fit strategy, in terms of system processor utilization and average waiting time under various system loads for rectangle requesting tasks with side lengths are powers of 2.