Processor Allocator (PA) is one of the main components to achieve high performance Chip Multiprocessors (CMPs). The task of the PA is to assign a set of processors to execute an incoming job scheduled by the Operating System (OS). An efficient PA is one that allocates an incoming job, if a suitable free submesh exists, with minimum overhead. In this paper, we propose a new contiguous processor allocation algorithm, Frame Combing with Memorization (FCM) for 2D mesh CMPs, which is fast, has complete submesh recognition, and assigns a set of processors without creating coverage areas for the incoming job. Our proposed algorithm outperforms other existing allocation strategies based on busy array approach such as Improved First Fit (IFF), and Better First Fit (BFF), or even Right of Busy Submeshes (RBS), a fast busy list based PA algorithm. Performance evaluation has been done with different job sets over different network sizes and at different network occupations. Our proposed PA is in average 3 up to 5 times faster than IFF, BFF and RBS for allocating small job (size 4x2) in a network size 10x10. For big network sizes (30x30), it is up to 60, 79, and 48 times faster than IFF, BFF, and RBS, respectively.