This paper proposes a trajectory generation method for mobile robots based on trajectory segment extension. The trajectory for mobile robot must be generated by depending on the conditions during the robot traveling. Such conditions to design the trajectory are given when the robot comes around those locations and are not provided before arriving around there. From this point of view, we have started to develop an on-line trajectory generation method based on extending the trajectory segment that is the low-order polynomial curve. We already proposed a trajectory extension approach calculated with sequentially designated waypoints in the absolute time. In this paper, we improved the method by utilizing the relative time expression for extension of the trajectory segment. Simulations with proposed method were done and the results were shown in this paper.