A procedure presented in this paper generates test sequences to check the conformity of an implementation with a protocol specification, which is modeled as a deterministic finite state machine (FSM). Given a FSM, a common procedure of test sequence generation, first, constructs a directed graph which edges include the state check after each transition, and produces a symmetric graph G* from and, finally, finds a Euler tour of G*. We propose a technique to determine a minimum-cost tour of the transition graph of the FSM. The proposed technique using Multiple Unique State Signature (MUSS) solves an open issue that one MUIO sequence assignment may lead to two more edges of unit cost being replicated to from G* while an optimal assignment may lead to the replication of a single edge of high cost. In this paper, randomly generated FSMs have been studied as test cases. The result shows that the proposed technique saves the cost 4∼28% and 2∼21% over the previous approach using MUIO and MUSP, respectively.