We proposed a new dominant point detection method.It has the following advantages: robustness, computational efficiency, and real-time response to pen movement. We construct a variable that is the ratio of the height to the width of an imagined rectangle whose bottom coincides with the polygon enclosed by the pen movement trace,and area is equal to the polygonal area. For we are on-line watching whether the value of this variable exceeds a given threshold, we can find dominant points in real-time. Only when the fluctuation comparing to the scale of a curve is big enough, value of this variable can exceed the given threshold. By this way, pseudo turning points can be rejected. As a new point comes in, only a small number of computations are needed to update the value of this variable. Effectiveness of this method was confirmed by experiments.