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The purpose of this paper is to prove that proper holomorphic self-mappings of the minimal ball are biholomorphic. The proof uses the scaling technique applied at a singular point and relies on the fact that a proper holomorphic mapping f : D → Ω with branch locus Vf is factored by automorphisms if and only if f∗(π1(D\f(f(Vf )), x)) is a normal subgroup of π1(Ω \ f(Vf ), b) for some b ∈ Ω \ f(Vf ) and x ∈ f−1(b).

Proper holomorphic self-mappings of the minimal ball