This research investigates the problem of area exploration using groups of unmanned aerial vehicles without service interruption under limited fuel constraints, where each group is assigned backup or search role depending on the situation. This paper presents an exhaustive search approach in finding a way to explore the search area with the least energy consumption. For this, the search length is divided into equal-sized intervals. The end points of these intervals can be designated as switch points where a search group goes back to the base to refuel and the backup group continues the job the returning group was doing before returning. This approach guarantees that the search operation is not interrupted by this switch operation for refueling. Since the exhaustive approach takes exponential time, a measure is proposed to determine the way to search the area that costs the least energy consumption for an allowed maximum execution time.