Communication reliability is a desired property in computer networks. One key technology to increase the reliability of a communication path is to provision a disjoint backup path. One of the main challenges in implementing this technique is that two paths that are disjoint at the IP or overlay layer may share the same physical links. As a result, although we may select a disjoint backup path at the overlay layer one physical link failure may cause the failure of both the primary and the backup paths. In this paper we propose a solution to address this problem. The main idea is to take into account the correlated link failure at the overlay layer More precisely, our goal is to find a route for the backup path to minimize the joint path failure probability between the primary and the backup paths. To demonstrate the feasibility of our approach, we perform extensive evaluations under both single and double link failure models. Our results show that, in terms of robustness, our approach is near optimal and is up to 60% better than no backup path reservation and is up to 30% better than using the traditional shortest disjoint path algorithm to select the backup path.