Path planning under 2D map is a key issue in robot applications. However, most related algorithms rely on point-by-point traversal. This causes them usually cannot find the strict shortest path, and their time cost increases dramatically as the map scale increases. So we proposed RimJump to solve the above problem, and it is a new path planning method that generates the strict shortest path for a 2D map. RimJump selects points on the edge of barriers to form the strict shortest path. Simulation and experimentation prove that RimJump meets the expected requirements.