Path setup considering QoS is one of the main problems to solve in Internet traffic engineering. In network restoration that is one of the traffic engineering components, to establish a backup path or backup path for a working path to be protected is the main task. The backup path should have enough bandwidth to guarantee the working paths. Thus this work requires the QoS routing solution that is to set up a backup path as well as a working path at the same time provisioning enough bandwidth. In this paper, we propose an algorithm to setup a backup path that shares the bandwidth of other backup paths whose working path does not pass along the same link with the working path we are considering. In this way we can reduce much bandwidth consumption caused by setting up backup paths. We also analyze the disjoint path computation algorithms. Finally we show simulation results how the algorithm can reduce the bandwidth consumption and how it will affect blocking when we setup paths.