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Let A be a C*-algebra which has no quotient isomorphic to M2(C). We show that for every orthogonally additive scalar nhomogeneous polynomials P on A such that P is Strong* continuous on the closed unit ball of A, there exists ϕ in A * satisfying that P (x) = ϕ(x n ), for each element x in A. The vector valued analogue follows as a corollary.doi:10.1093/qmath/ham042 fatcat:5tac4jhtcvcf3clsm67qfhr55m