In this paper, we proposed a new multicast algorithm which is efficiently applicable to overlapped process group environments where one process may be involved in several process groups. Unlike the esisting algorithms, the proposed one provides an efficient group communication mechanism by generating the processgroup information in two-level tree. Using this algorithm, we improved the shortcoming of the existing algorithms by reducing the overhead in passing through unnecessary processes for message ordering. We have provided the causal ordering method as well as the total ordering method in group communication environments. As a result, we allow one process to deliver message to other processes with a short delay time, and reduced the overhead required for the message ordering. Also, we logically proved the proposed causal ordering method, and compared the performance of the proposed algorithm with ones of other existing algorithms by computer simulation.