Traffic management at road intersections is a complex requirement that has been an important topic of research and discussion. Solutions have been primarily focused on using vehicular ad hoc networks (VANETs). Key issues in VANETs are high mobility, restriction of road setup, frequent topology variations, failed network links, and timely communication of data, which make the routing of packets to a particular destination problematic. To address these issues, a new dependable routing algorithm is proposed, which utilizes a wireless communication system between vehicles in urban vehicular networks. This routing is position-based, known as the maximum distance on-demand routing algorithm (MDORA). It aims to find an optimal route on a hop-by-hop basis based on the maximum distance toward the destination from the sender and sufficient communication lifetime, which guarantee the completion of the data transmission process. Moreover, communication overhead is minimized by finding the next hop and forwarding the packet directly to it without the need to discover the whole route first. A comparison is performed between MDORA and ad hoc on-demand distance vector (AODV) protocol in terms of throughput, packet delivery ratio, delay, and communication overhead. The outcome of the proposed algorithm is better than that of AODV.