Abstract: In the analysis of composite motion for points, the kinematic analysis of the transport point is the key for decomposing or synthesizing the motion of moving point. The transport point is the point on the moving coordinate system that coincides with the moving point instantaneously. In this paper, it is pointed out that at any time, the transport point is a “fixed” point on the moving coordinate system and it only moves with the moving coordinate system. This paper presents an analytic method of expressing velocity and acceleration of transport point, and it also derives the synthesis theorem of velocity and acceleration of moving point. This method does not need to introduce the relative derivative, hence it avoids the difficulty within the derivation method of displacement or relative derivative, which is hard to understand for students.