To establish a formal inferential system of intention consequences is an important issue in the formal study of intention. In this paper, a new formal system of intention consequences L_m5c based on "reduced implication" is proposed which provides a norm of intention consequences. Compared with other known formal systems of intention consequences, this system is simpler and possesses many desired properties, such as free from all cases of the known side-effects. Besides, it is powerful in reasoning about intention so that the agent itself can use it to perform tasks such as intention inference and goal revsing.