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 $V_f$ is factored by automorphisms if and only if $f_{*}\left(\pi ₁(D\setminus f^{-1}\left(f\left(V_f\right)\right),x)\right)$ is a normal subgroup of $\pi ₁(\Omega \setminus f\left(V_f\right),b)$ for some $b\in \Omega \setminus f\left(V_f\right)$ and $x\in f^{-1}\left(b\right)$.