Abstract: Let A be a factor von Neumann algebra acting on a Hilbert space H with dim H >1. With the help of method of algebraic decomposition, we prove that if a nonlinear map δ: A→A satisfies (A·B·C)=(A)·B·C+A·(B)·C+A·B·(C) for any A,B,C∈A, then  is an additive *derivation.

Key words: factor von Neumann algebra, nonlinear skew Jordan triple derivable map, *-derivation