Wireless sensor networks are composed of hundreds or thousands of small nodes called sensor that work together and are associated with a specific task or tasks to do. Each of these nodes includes sensor, processor, communication components, a small memory and a source of energy.It is expected that wireless sensor networks will be used widely in many applications in near future. Scalability and lifetime extension in wireless sensor networks are critical issues in designing and implementing a wireless Sensor Network (WSN).Relay Nodes (RNs) in WSN are nodes with higher useful power and radius, which considered as head of network. RNs are able to disseminate data in a higher level, network clusters, and network regions. In this paper, a novel algorithm is proposed to cover all sensor nodes with the least possible RNs. The number of RNs can be calculated through a proposed mathematical function which has the maximum rate of detection. The proposed approach shows high capability for fault tolerance in WSN when compared to other algorithms. Manuscript profile