Longest Job First (LJF), the opposite of Shortest Job First, has been an unpopular process scheduling algorithm. The idea of combinational burst time was used to avoid the starvation problem associated with the LJF algorithm and to make it compete with other scheduling algorithms with respect to some performance metrics. Although the combinational burst time proposal led to improved performance, the work suffers from the limitations that the average waiting time and the average turnaround time were slightly higher, and the number of context switches was a little higher also. The research reported in this dissertation addressed these shortcomings by proposing a new scheduling algorithm that enhanced the combinational burst time model by using median as a statistics of central tendency and assigning the processors to the CPU in interleave order. The proposed algorithm was implemented and compared with First Come First Serve (FCFS), Longest Job First (LJF), Longest Job First with combinational model (LJF+CBT) and Shortest Job First (SJF) scheduling algorithms using varying number of processes and burst times. Results from the experiments showed that the enhanced LJF+CBT outperformed the existing LJF+CBT producing 26.69% better average waiting time (AWT), 21.77% better average turnaround time (ATAT) and 14.29% better number of context switches (CS). In Longest Job First (LJF) scheduling this algorithm drastically reduced the average waiting time by 46.5%, average turnaround time by 39.39% and number of context switching between processes by 33.33% for all the number of processes used. Sequel to these results, a better solution to starvation problem in Longest Job First scheduling algorithm was proffered.