A vector timestamp is used to satisfy message ordering in a group communications. In this paper, we propose a new vector timestamp compression method which is applicable to a single process group environment where one process belongs to only one precess group. An existing compression method compares the fields of the previously sent vector timestamp with thouse of the currently updated vector timestamp, then sends only the modified fields of the vector timestamp. Unlike the previous one, a proposed compression method performs individual compression for each process using the locally maintained vector timestamp information on other processes. Also, we logicallyproved the causal ordering algorithm using the new compression method and compared the performance of the proposed method with one of the previous compression method by computer simulation. Using the proposed compression method, the message overhead required for causal ordering can be reduced.