This letter proposes a post-processing method to improve the smoothness and safety of the path for an autonomous vehicle navigating in an urban environment. The proposed method transforms the initial path given by local path planning algorithms using a stochastic approach to improve its smoothness and safety. Using the proposed method, the initial path is efficiently transformed by iteratively updating the position of each waypoint within it. The proposed method also guarantees the feasibility of the transformed path. Experimental results verify that the proposed method can improve the smoothness and safety of the initial path and ensure the feasibility of the transformed path.