Let A and B be two C∗-algebras such that A is prime. In this paper, we investigate the additivity of maps from A onto B that are bijective and satisfy (A∗B + BA∗) = (A)∗(B) + (B)(A)∗ for all A,B ∈ A where is a non-zero scalar such that 6= ±1. Moreover, if (I) is a projection, then is a ∗-isomorphism.
