In the previous report, the author introduced a new method to determine the manoeuvring characteristics of ships by means of some kinds of the phase portraits. However, it cannot be said that the proposed method is absolutely perfect. Because it is very tedious for the trajectory of manoeuvring motion to reach the limit cycle even in case of stable ships, and accordingly in case of unstable ships it often becomes impossible to continue the modified zigzag manoeuvre up to the limit cycle, so that the proposed method becomes invalid. Hence, in this report, the author modifies the previous method so that it may become applicable for an arbitary section of the trajectory on the phase portrait. The validity of this modified method is proved by simulation studies as well as by good agreement between the trajectories measured on board and those of the model identified by this method. If this modified method is used, it becomes unnecessary to carry out the two kinds of the modified zigzag tests to determine the manoeuvring characteristics.