Multiplicative ∗-Lie isomorphisms between factors

Let M, N be factors. If Φ:M→N is a multiplicative ∗-Lie isomorphism, then Φ is of the form σ+τ, where σ is a linear ∗-isomorphism, or a conjugate linear ∗-isomorphism, or the negative of a linear ∗-anti-isomorphism, or the negative of a conjugate linear ∗-anti-isomorphism of M onto N and τ is a mapping of M into CI={λI|λ∈C} which maps commutators into zero.