The shortest-path searching algorithm must not only find a global solution to the destination, but also solve a turn penalty problem (TPP) in an urban road transportation network (URTN). Although the Dijkstra algorithm (DA) as a representative node-based algorithm secures a global solution to the shortest path search (SPS) in the URTN by visiting all the possible paths to the destination, the DA does not solve the TPP and the slow execution speed problem (SEP) because it must search for the temporary minimum cost node. Potts and Oliver solved the TPP by modifying the visiting unit from a node to the link type of a tree-building algorithm like the DA. The Multi Tree Building Algorithm (MTBA), classified as a representative Link Based Algorithm (LBA), does not extricate the SEP because the MTBA must search many of the origin and destination links as well as the candidate links in order to find the SPS. In this paper, we propose a new Link-Based Single Tree Building Algorithm in order to reduce the SEP of the MTBA by applying the breaking rule to the LBA and also prove its usefulness by comparing the proposed with other algorithms such as the node-based DA and the link-based MTBA for the error rates and execution speeds.