Let F(m)n(L;$\sqrt{-1})$ be the m-th derivative of the n-th coefficient polynomial Fn(L;a) of the Kauffman polynomial F(L; a,z) of a link L evaluated at $a=\sqrt{-1}$. T. Kanenobu proved that its order is no more than m+n if m+n>0, m>0. In this talk, we show that its order is just m+n.