Let A be a semi-finite factor von Neumann algebra. We prove that if a map δ : A → A satisfies that for any A , B ∈ A there is a linear derivation δ A , B : A → A such that δ ( A ) B + Aδ ( B ) = δ A , B ( AB ) , then δ is a linear derivation. It is a positive answer to the problem on semi-finite factor von Neumann algebra posed by Molnár in the paper [A new look at local maps on algebraic structures of matrices and operators, New York J Math 28 (2022)].