Let A and B be two von Neumann algebras. For A, B ∈ A, define by [A, B] * = AB − BA * and A • B = AB + BA * the new products of A and B. Suppose that a bijective map Φ : A → B satisfies Φ([A • B, C] *) = [Φ(A) • Φ(B), Φ(C)] * for all A, B, C ∈ A. In this paper, it is proved that if A and B be two von Neumann algebras with no central abelian projections, then the map Φ(I)Φ is a sum of a linear *-isomorphism and a conjugate linear *-isomorphism, where Φ(I) is a self-adjoint central element in B with Φ(I) 2 = I. If A and B are two factor von Neumann algebras, then Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism