In this paper, we present a preemptive joint scheduling of hard deadline periodic and hard deadline aperiodic tasks on a uniprocessor real-time system. The scheduling has extended the Critical Task Indicating (CTI) algorithm [4] of which simulation study shows a considerable performance improvement over the other soft aperiodic task schedulings, especially under a heavy transient overload. Since a hard deadline aperiodic task has its own deadline, the proposed algorithm has a decision making mechanism that performs the on-line acceptance/rejection test upon its arrival. For simplicity and good performance, the algorithm reuses the original CTI table being used in the CTI algorithm as a slack search domain. Moreover, by searching the CTI table similarly to a circular list, it has removed the problem of search space limitation caused by the hyperperiod bound.