Wireless sensor networks are utilized in many different areas such as health, agriculture, security, and entertainment. Since the nodes that constitute wireless sensor networks have limited energy resources, many studies have been carried out on use of their resources in an energy efficient manner. These studies generally focused on duty cycle techniques or constructing energy efficient communication backbones. In wireless sensor systems, the connected dominating sets are generally considered to be used as a backbone. In addition, the deployment of the nodes that harvest their own energy in wireless sensor networks has also been considered in recent studies. In this study, a new distributed algorithm is proposed to construct reusable connected dominating set for wireless networks that possess energy harvester nodes and ordinary nodes which could not harvest its energy. Whenever an energy depletion problem in a node or in more than one node occurs, after a specific interval, the proposed algorithm is re-employed on the alive nodes unless wireless sensor network is disconnected. The proposed algorithm was implemented on SensEH simulation environment based on Cooja which is one of the most commonly used tools in the wireless sensor network area. The new algorithm and the rival algorithm in the area are analyzed with respect to the lifetime of the systems together with the time and the energy consumptions required by the algorithms. According to the results, it is observed that the proposed algorithm can double the total lifetime compared to the rival algorithm.