The Leader Election Algorithm is used to select a specific node in distributed systems. In the case of Wireless Sensor Networks, this node can be the one having the maximum energy, the one situated on the extreme left in a given area or the one having the maximum identifier. A node situated on the extreme left, for instance, can be used to find the boundary nodes of a network embedded in the plane. The classical algorithm allowing to find such a node is called the Minimum Finding Algorithm. In this algorithm, each node sends its value in a broadcast mode each time a better value is received. This process is very energy consuming and not reliable since may be subject to an important number of collisions and lost messages. In this paper, we propose a new algorithm called LOGO (Local Optima to Global Optimum) where some local leaders will send a message to a given node, which will designate the global leader. This process is more reliable since broadcast messages are sent only twice by each node, and the other communications are based on a direct sending. The obtained results show that the proposed algorithm reduces the energy consumption with rates that can exceed 95% compared with the classical Minimum Finding Algorithm.