Coverage and energy conservation are two major issues in wireless sensor networks (WSNs), especially when sensors are randomly deployed in large areas. In such WSNs, sensors are equipped with limited lifetime batteries and redundantly cover the target area. To face the short lifetime of the WSN, the objective is to optimise energy consumption while maintaining the full sensing coverage. A major technique to save the energy is to use a wake-up scheduling protocol through which some nodes stay active whereas the others enter sleep state so as to conserve their energy. This study presents an original algorithm for node selfscheduling to decide which ones have to switch to the sleep state. The novelty is to take into account the remaining energy at every node in the decision of turning off redundant nodes. Hence, the node with a low remaining energy has priority over its neighbours to enter sleep state. The decision is based on a local neighbourhood knowledge that minimises the algorithm overhead. To verify and evaluate the proposed algorithm, simulations have been conducted and have shown that it can contribute to extend the network lifetime. A comparison with existing works is also presented and the performance gains are highlighted.