Let A be a prime ∗-algebra with unit I and a nontrivial projection. Then the map Φ : A → A satisfies in the following condition Φ(A ⋄ B) = Φ(A) ⋄ B + A ⋄ Φ(B) where A⋄ B = A∗B −B∗A for all A, B ∈ A, is additive. Moreover, if Φ(αI) is self-adjoint operator for α ∈ {1, i} then Φ is a ∗-derivation.
