This paper presents a submesh allocation scheme for two-dimensional mesh systems. The submesh detection process considers only those available free submeshes that border from the left on some allocated submeshes or have their left boundaries aligned with that of the mesh. Fragmentation in the system can be reduced as a result. More importantly, we present an efficient approach to facilitate the detection of such available submeshes. The basic idea of the approach is to place the allocated submeshes of the busy set in a certain order so as to reduce the complexity of subtraction operations required for submesh detection. The method is simple and causes an amount of overhead which is only a fraction of that produced by previous algorithms. Extensive simulation has been conducted to evaluate the performance of the proposed scheme. The results show that when allocation overhead is considered, the proposed scheme may outperform previous methods.