The A* algorithm and its modifications are commonly used in graph searching for mobile robot path planning. However in case of large open list sizes the A* algorithm needs significant time to find the solution due to the open list sorting procedure which determines the computational complexity of A*. This paper presents a new approach called L* which improves the A* graph searching algorithm and provides linear computational complexity due to the lack of the open list sorting procedure. This is a crucial factor in order to decrease the time consumption for large open list sizes in a graph searching algorithm.