Routing overlay offers an ideal methodology to improve the end-to-end communication performance by deriving a backup path for any node pair. This paper focuses on a challenging issue of selecting a proper backup path to bypass the failures on the default path with high probability for any node pair. For existing backup path selection approaches, our trace-driven evaluation results demonstrate that the backup and default paths for any node pair overlap with high probability and hence usually fail simultaneously. Consequently, such approaches fail to derive a robust backup path that can take over in the presence of failure on the default path. In this paper, we propose a three-phase RBPS approach to identify a proper and robust backup path. It utilizes the traceroute probing approach to obtain the fine-grained topology information, and systematically employs the grid quorum system and the Bloom filter to reduce the resulting communication overhead. Two criteria, delay and fault-tolerant ability on average, of the backup path are proposed to evaluate the performance of our RBPS approach. Extensive trace-driven evaluations show that the fault-tolerant ability of the backup path can be improved by about 60%, while the delay gain ratio concentrated at 14% after replacing existing approaches with ours. Consequently, our approach can derive a more robust and available backup path for any node pair than existing approaches. This is more important than finding a backup path with the lowest delay compared to the default path for any node pair.