Nowadays, there is a greater need for energy efficient and stable underwater sensor networks (UWSNs). Underwater sensors usually do not have enough power, so the goal of underwater sensor networks is to make the network have a long lifetime. An underwater heterogeneous sensor network (UWHSN) is one way to cluster the sensors, and the application of UWHSNs is simple and fast, but robots, lifetime and energy-partition are all drawbacks of UWHSNs. In this paper we propose the underwater isomorphic sensor network (UWISN) clustering technology. By analyzing the characteristics of UWISNs, we determine that an UWISN has strong expansibility, mobility, energy-efficiency and long lifetime. An UWISN adopts normal sensor nodes to be cluster heads, and these cluster heads communicate with each other. This paper seeks the optimal number of clusters and uses FCM to elect cluster heads and establish the network. In addition, an idea of real cluster heads and the method to elect them have been proposed. Finally, the simulation results show that the solution is effective and UWISNs can improve the energy consumption of an UWSN.