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With the development of ad hoc networks, some researchers proposed several geometric routing protocols which depend on the planarization of the network connectivity graph to guarantee the delivery of the packet between any pair of nodes in the network. In this paper, we proposed a new online routing algorithm GLNFR (greedy and local neighbor face routing) for finding paths between the nodes of the ad hoc networks by storing a small amount of local face information at each node. The localized Delaunay triangulation was used to be the backbone of wireless network on which the GLNFR routing algorithm runs. It has the better scalability and adaptability for the change of ad hoc networks. Experiment on NS have been conducted. The results show that the delivery rate of packets and routing protocol message cost under such novel routing protocols performs better than others proposed before.