In this paper, we propose a routing technique to alleviate packet loss due to transient link failures, which are major causes of disruption in the Internet. The proposed technique based on Alternate Next Hop Counters (ANHC) allows routers to calculate backup paths and re-route packets accordingly, thereby bypassing transient failures. This technique guarantees full repair coverage for single link failures, without significantly changing the way traditional routing works and with minimal impact on the computation and memory requirements for routers. We evaluate the performance of our proposed ANHC approach through extensive simulations and show that the stretch of its pre-computed alternate paths, its failure-state link load increase, and its computational and memory overheads are minimal.