In this paper, we introduce the concept of ternary antiderivation on ternary Banach algebras and investigate the stability of ternary antiderivation in ternary Banach algebras, associated to the (alpha, ss)-functional inequality parallel to.F(x + y + z) - F(x + z) - F(y - x + z) - F(x - z)parallel to <=parallel to alpha(F(x + y - z) + F(x - z) - F(y))parallel to +parallel to ss(F(x - z) + F(x) - F(z))parallel to where a and ss are fixed nonzero complex numbers with |alpha|+ |ss| < 2 by using the fixed point method.