Traditional survivable network design assumes that at any time at most a single link or node fails. In optical networks, a single point of failure may lead to the failure of multiple links. In this paper, we consider the design of an optical network that can survive the failures of any two neighboring links. We present a loopback recovery method that requires the computation of backup paths for each link. An optimal algorithm for computing the backup paths is presented. Numerical results comparing the performance of our algorithm with other loopback approaches indicate that a slight increase in capacity can achieve 100% protection under this failure model.