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Real time scheduling algorithms provide a mean to schedule tasks on processor such that real time constraints are guaranteed. Fixed priority real time scheduling algorithms have low runtime complexity and their behaviour can be categorized a prior but they do not support dynamic systems very well. A transient overload in dynamic priority scheduling algorithms may cause a critical task to fail but they are capable of supporting dynamic systems. Hybrid scheduling algorithm's behaviour can be categorized a prior and they support dynamic systems as well but they may unnecessarily cause non critical tasks to miss their deadlines even when all critical tasks are schedulable. This paper proposes an algorithm called real urgency first scheduling (RUF) algorithm. According to this algorithm, critical tasks are always guaranteed to meet their real time constraints while improving the execution of non critical tasks.