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Computing one-to-one shortest paths on road networks is a fundamental work in many practical applications, especially in network and transportation related analyses. Pallottino's graph growth algorithm implemented with two queues (TWO-Q) is recommended as one of the top candidates to this kind of problems in literature. However, as a label-correcting shortest path algorithm, original TWO-Q algorithm begins scan from the source node and has to travel the whole network before it gets the final result no matter how close the destination is. Compared with label-setting shortest path algorithms, TWO-Q spends a lot of time on useless work when the shortest path is relatively short. To overcome this shortcoming, this paper presents an improved version of TWO-Q algorithm which is useful for path routing on road networks This algorithm, named Minimum Label Delimiting TWO-Q algorithm(MiLD-TWO-Q), traces the minimum label inside the two queues storing the candidate nodes, and terminates once the label of destination node is not larger than the minimum label. Experimental results show that the new algorithm overcomes the shortage of TWO-Q when the shortest path is relatively short and inherits the advantage of TWO-Q when the shortest path is relatively long. Hence MiLD-TWO-Q is more efficient and advisable for finding one-to-one shortest paths on road networks.