Recently, collaborative works are increased more and more over the distributed heterogeneous computing environments. The availability of high-speed wide-area networks has also enabled collaborative multimedia applications such as video conferencing, distributed interactive simulation and collaborative visualization. Distributed high performance computing and collaborative multimedia applications, it is extremely important to efficiently perform group communication over a heterogeneous network. Typical group communication patterns are broadcast and Multicast. Heuristic algorithms such as FEF, ECEF, look-ahead make up the message transmission tree for the broadcast and multicast over the distributed heterogeneous systems. But, there are some shortcomings because these select the optimal solution at each step, it may not be reached to the global optimum In this paper, we propose a new heuristic algerian that constructs tree for efficiently collective communication over the previous heterogeneous communication model which has heterogenity in both node and network. The previous heuristic algorithms my result in a locally optimal solution, so we present more reasonable and available criterion for choosing edge. Through the performance evaluation over the various communication cost, improved heuristic algorithm we proposed have less completion time than previous algorithms have, especially less time complexity than look-ahead approach.