Among all non-blocking non-preemptive scheduling techniques for mesh-connected multicomputer system to ensure contiguous processor allocation, Largest-Job-First (LJF) technique proves to be one of the best in achieving small latency compared to others such as First-Come-First-Serve (FCFS) and Smallest-Job-First (SJF). We notice that LJF prevails when there is a significant variance in the number of processors requested among jobs. Instead, if the variance is relatively small, the merit of LJF is overshadowed by its inherent disadvantage in approaching bypass limit faster than the simpler FCFS one. Thus, the size-order used by the LJF for scheduling should be weighed less versus the arriving-order used by the FCFS whenever the variance is smaller. This paper proposes a novel scheduling technique to self-adjust in real-time between the two orders according to the size variance among the jobs in the queue. This technique ensures that the advantage of the LJF is preserved while significantly diminishing the chance for the blocking situation to occur. Our simulation results consistently show an significant improvement from our technique over the LJF and the FCFS ones.