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Underwater wireless sensor network (UWSN) features many unique characteristics, including slow propagation speed, high endto-end delay, low available bandwidth, variable link quality, and energy constraint. All these problems pose a big challenge to devise a transmission efficient, energy-saving, and low delay routing protocol for UWSNs. In this paper we devise a relative distance based forwarding (RDBF) routing protocol, which aims to provide transmission efficient, energy-saving, and low delay routing. We utilize a fitness factor to measure and judge the degree of appropriateness for a node to forward the packets. Under the limitations of the fitness factor, RDBF can confine the scope of the candidate forwarders and find the beneficial relays to forward packets. In this way, only a small fraction of nodes are involved in forwarding process, which can distinctly reduce the energy consumption. Moreover, using only the selected beneficial nodes as forwarders can both enhance the transmission efficiency and reduce the end-to-end delay. This is because the distances of these nodes to the sink are the shortest and the hop counts of routing paths consisted by these nodes are minimum. We use the ns-2 based simulator to conduct our experiment; the results show that RDBF performs better in terms of packet delivery ratio, end-to-end delay, and energy efficiency.