Abstract: The question how to choose the centroid in the theorem of the angular momentum has been discussed for thirty years(see references 1~4). This paper gives a unified statement of the theorems of the change in the angular momentum of a system of particles. Especially, We develop the theorem of the angular momentum of a system of particles with respect to the centre of instontaneous zero velocity, in general, it is considered impossible.Using this theorem, we solve an example, the solution of which in this way was considered impossible.