It has been required more reliable communication on processes and improvement of system performance as distributed systems using multicast protocol became widespread. In distributed environment maintaining data consistency through asynchronous execution of processes and coordinating the activities of them would occurs. This paper proposes a total ordering algorithm, TORMP, in order to resolve these problems. TORMP takes advantage of multicast protocol and uses an effective token passing method. It reduces a process delaying time before transmitting its message by multicasting a token simultaneously to every process that initiates the request of the message. Moreover, the processes receiving the token start multicasting the message at the same time, which causes to cut down the overall transmission dely. In case that one process sends a message, TORMP hardly uses the procedure of controlling for ordering. It gives fairly the right of sending messages to all processes in a group with utilizing vector clock. In TORMP, unlike other algorithms, the number of packets generated during ordering process does not depend on the number of processes.