Low confusion coefficient values can make side-channel attacks harder for vector Boolean functions in Block cipher. In this paper, we give new results of confusion coefficient for f ⊞ g, f ⊡ g, f ⊕ g and fg for different Boolean functions f and g, respectively. And we deduce a relationship on the sum-of-squares of the confusion coefficient between one n-variable function and two (n - 1)-variable decomposition functions. Finally, we find that the confusion coefficient of vector Boolean functions is affine invariant.