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Several studies have found some properties of Internet such as Triangle Inequality Violations (TIVs). The studies have reported the existence of TIV in the Internet delay space. Triangle inequality violations that are important to peer-to-peer applications can be leveraged to build overlay routing to improve peer-to-peer performance. How to select relay nodes becomes a crucial factor to overlay routing. In this paper, we propose a scheme called Relay Service Scheme (RSS) that takes AS connecting degree and AS valley-free counts into account. We then verify the performance of the scheme with available Internet delay data set. The results demonstrate that AS connecting degree and AS valley-free counts are meaningful to relay server selection and can be utilized in building relay service to decrease about 33%-50% probing throughput in contrast to ASAP as well as improve P2P performance. It is the first scheme to pick up relay as stable and reusable servers to form a relay network. It is believed that the advantage can be used by network operator to arrange the relay servers at proper location and provide the P2P applications both good QoS performance and low overhead.