The Leader Election in Wireless Sensor Networks depends on the nature of the application domain, the use case and the energy consumption. In the case of real time applications, the choice will be based on the speed of the election, and in the case where time is not important, the choice will be based on the energy consumption. The classical algorithm allowing to elect 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 it is subject to an important number of collisions and lost messages. In this paper, we propose a new algorithm called BROGO (Branch Optima to Global Optimum) where after finding a spanning tree of a WSN, each leaf will route a message through its branch to the root in order to find the leader in that branch. The root will then elect the global leader from the received branch leaders. This process is more reliable since there is a small number of broadcast messages and a reduced number of nodes that send broadcast messages at the same time. The obtained results show that the proposed algorithm reduces the energy consumption with rates that can exceed 95\% when compared with the classical Minimum Finding Algorithm. Its message and time complexity is equal to O(n).