The paper presents a method for deriving a complete test suite for a timed deterministic FSM with time-outs when only the upper bound on the number of states and the largest finite time-out at a state of an implementation under test are known. We also show that a test suite derived for a corresponding classical FSM is much longer than this obtained directly from a FSM with time-outs. The application to a case study, the Loan Approval Service, illustrates how our approach can be applied for deriving tests for compositions of timed FSMs