The state-of-the-art graph searching algorithm applied to the optimal global path planning problem for mobile robots is the A* algorithm with the heap structured open list. In this paper, we present a novel algorithm, called the L* algorithm, which can be applied to global path planning and is faster than the A* algorithm. The structure of the open list with the use of bidirectional sublists (buckets) ensures the linear computational complexity of the L* algorithm because the nodes in the current bucket can be processed in any sequence and it is not necessary to sort the bucket. Our approach can maintain the optimality and linear computational complexity with the use of the cost expressed by floating-point numbers. The paper presents the requirements of the L* algorithm use and the proof of the admissibility of this algorithm. The experiments confirmed that the L* algorithm is faster than the A* algorithm in various path planning scenarios. We also introduced a method of estimating the execution time of the A* and the L* algorithm. The method was compared with the experimental results.