This paper develops an efficient exact graph-coloring algorithm based on Maximum Independent Set (MIS) for allocating processors in distributed systems. This technique represents the allocated processors in specific time in a fully connected graph and prevents each processor in multiprocessor system to be assigned to more than one process at a time. This research uses a sequential technique to distribute processes among processors. Moreover, the proposed method has been constructed by modifying the FMIS algorithm. The proposed algorithm has been programmed in Visual C++ and implemented on an Intel core i7. The experiments show that the proposed algorithm gets better performance in terms of CPU utilization, and minimum time for of graph coloring, comparing with the latest FMIS algorithm. The proposed algorithm can be developed to detect defected processor in the system.