Path following is a popular task for robotic use. The conventional approach for the path following consists of two stages. At the first stage, the desired state of a robot is computed as a function of time before the robot executes the task. And at the second stage, the robot is controlled to track the desired state. Since the objective of the original task is to follow the reference path, the velocity of the robot or timing is not needed to be controlled strictly. In this paper, a new approach to make the robot follow the reference path is proposed. This approach defines the desired state as a function of a parameter φ, which has a dynamics. By using a Lyapunov function, the global asymptotic stability of the system is proved. Computer simulations show the effectiveness of the proposed method.