Testing strategies based on finite states machines (FSMs) are widely used for protocol test derivation. Most FSM-based methods of test generation are based on the well-known W-method. In this paper, we determine the necessary conditions for a test suite to be complete under an assumption that only the number of states of an implementation under test is known. Based on the above conditions, we propose a novel modification of the W-method for the complete test suite derivation. We also present the results of computer experiments that clearly show that the total length of a test suite returned by the proposed modification is close to the minimal.