The paper is devoted to deriving finite test suites with guaranteed fault coverage for Input / Output automata using the ‘black-box’ model when only the upper bound on the number of states of an implementation automaton under test is known but there is no knowledge about its structure. We propose a methods for deriving a finite State Machine (FSM) for a given automaton and show that finite tests derived by the known FSM based test suites without explicit enumeration of implementation automata are complete with respect a number of fault models.