Let J(f) denote the Julia Fatou set of the rational function f and let G be a simply connected invariant component of its complement. Let h map the unit diskDcanformally onto G. We consider the connection betwen the repulsive fixed points ζ∈G of f and the fixed points δ∈∂Dof the finite Blaschkc product ϕ=hf h. We show in particular that h has an angular limit ζ=h(δ) at δ and give an inequality relating f″(ζ) and ϕ′(δ1where h(δ1)=ζ.