A modified version of Local Remaining Execution-TL (LRE-TL) real-time multiprocessor scheduling algorithm is presented. LRE-TL uses two events to make scheduling decisions: The Bottom (B) event and the Critical (C) event. Event B occurs when a task consumes its local utilization meaning that it has to be preempted. Event C occurs when a task’s local laxity becomes zero meaning that the task should directly be scheduled for execution. Event C always results in a task migration, therefore we modified the initialization procedure of LRE-TL to select the tasks that have a higher probability of firing a C event to be scheduled for execution firstly, and thereby tasks migration will be reduced. We have conducted an independent-samples t test to compare tasks migration using the original LRE-TL algorithm and the modified algorithm. The results obtained showed that there was a significance reduction in tasks migration when the proposed solution is applied.