Real-time systems are often designed using preemptive scheduling to guarantee the execution of high priority tasks. For multiple reasons there is a great interest in exploring non-preemptive scheduling in the case of hard real-time systems where missing deadline leads to catastrophic situations. This paper presents a necessary and sufficient schedulability condition for determining whether a task will satisfy its period and precedences constraints when some tasks have already been scheduled. Tasks we are dealing with are non-preemptive and the periods considered here are strict.