The behavior of real-time systems depends not only on their interaction with the environment but also on very rigid time constraints that puts restrictions on when these interactions take place. The timing aspect of such systems renders the testing process difficult without defining adequate test selection criteria that ensure good coverage of the system while keeping the number of needed test cases considerably low. In this paper, we propose a method for testing real-time systems, formally modeled as Timed Input Output Automata (TIOA), which aims at generating a set of test cases that would allow us to check every transition of the TIOA as soon as possible, as late as possible, and at the middle between these two executions. The execution times of every transition are determined based on the minimum and maximum delays between the source state of the transition and its clock guards.