Overlay Multicast is a promising approach to overcome the implementation problem of IP multicast. Real time services like Internet broadcasting are provided by the overlay multicast technology due to the complex nature and high cost of IP multicast. To reduce frequent updates of multicast members and to support real time service without delay, we suggest a reliable overlay multicast tree based on members’ sojourn probabilities. Path reliabilities from a source to member nodes are considered to maximize the reliability of an overlay multicast tree. The problem is formulated as a binary integer programming with degree and delay bounds. A tabu search heuristic is developed to solve the NP-complete problem. Outstanding results are obtained which is comparable to the optimal solution and applicable in real time.