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We propose an efficient multipath routing algorithm for a given quality of service (QoS) in carrying delay-sensitive traffic. The proposed algorithm takes advantage of available alternate routes that can be used in the network without violating end-to-end delay and bandwidth constraint. The objective of our routing scheme is to minimize the maximum of link utilization. For an arriving connection request, a set of feasible paths is found without re-routing the existing traffic flows and the corresponding ratio in allocation of traffic for each path is determined. The algorithm is very efficient and can be used for the arrival connection request on-the-fly. Extensive simulation results show that 13-27% gains of additional connections can be achieved when compared to the shortest path routing.