In this paper we proposed a new map construction and path planning method for mobile robot. In our proposed method first we introduced triangular representation map that mobile robot can navigate through shorter path and flexible motion instead of grid representation map for mobile robot navigation. method in which robot can navigate complete space through as short path as possible in unknown environment is proposed. Finally we proposed new path planning method in a quadtree representation map. To evaluate the performance of our proposed new path planning method in a quadtree representation map. To evaluate the performance of our proposed triangular representation map it was compared with the existing distance transform path planning method. And we considered complete coverage navigation and new path planning method through several examples.