In long distance sensor nodes, propagation delay is the most crucial factor for the successful transmission of data packets in underwater acoustic sensors networks (UWAs). Therefore, to cope with the problem of propagation delay, we propose examining and selecting the best relay node (EBRN) technique based on checking the eligibility and compatibility of RN and selecting the best RN for UWAs. In the EBRN technique, the source node (S) creates a list of the best RNs, based on the minimum propagation delay to the midpoint of a direct link between S and the destination node (D). After that, the S attaches the list of selected RNs and transmit to the D along with data packets. Finally, from the list of selected RNs, the process of retransmission is performed. To avoid collision among control packets, we use a backoff timer that is calculated from the received signal strength indicator (RSSI), propagation delay and transmission time, whereas the collision among data packets is avoided by involving single RN in a particular time. The performance of the proposed EBRN technique is analyzed and evaluated based on throughput, packet loss rate (LR), packet delivery ratio (PDR), energy efficiency, and latency. The simulation results validate the effectiveness of the proposed EBRN technique. Compared with the existing schemes such as underwater cooperative medium access control (UCMAC) and shortest path first (SPF), the proposed EBRN technique performs remarkably well by increasing the throughput, PDR, and energy efficiency while decreasing the latency and LR in UWAs.