This paper develops an efficient exact graph-coloring algorith m based on Maximu m 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 mu ltiprocessor system to be assigned to more than o ne process at a time. This research uses a sequential technique to distribute processes among processors . Moreover, the proposed method has been constructed by modify ing the FMIS algorithm. The proposed algorith m 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 min imu m t ime for of graph coloring, comparing with the latest FMIS algorith m. The proposed algorithm can be developed to detect defected processor in the system.