In wireless sensor networks (WSNs) with symmetric duty cycles, a block design technique produces an optimal solution for neighbor discovery in terms of the worst-case discovery latency. However, block design-based neighbor discovery methods may not be applicable to WSNs with asymmetric duty operations. Thus, to address this lack of support of asymmetric WSNs, we propose a new neighbor discovery protocol (NDP) that combines two block designs for generating a set of discovery schedules. We prove that the discovery schedule generated by the proposed NDP includes at least one common active slot with any neighboring nodes within a single cycle. We also conduct a simulation study and show that the proposed NDP is better than representative NDPs such as U-Connect, Disco, SearchLight, Hedis, and Todis in terms of discovery latency and energy efficiency.