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Milnor proved that the moduli space Md of rational maps of degree d ≥ 2 has a complex orbifold structure of dimension 2(d − 1). Let us denote by 
${\mathcal S}$ d the singular locus of Md and by 
${\mathcal B}$ d the branch locus, that is, the equivalence classes of rational maps with non-trivial holomorphic automorphisms. Milnor observed that we may identify M2 with ℂ2 and, within that identification, that ${\mathcal B}$ 2 is a cubic curve; so ${\mathcal B}$ 2 is connected and ${\mathcal S}$ 2 = ∅. If d ≥ 3, then it is well known that ${\mathcal S}$ d = ${\mathcal B}$ d . In this paper, we use simple arguments to prove the connectivity of ${\mathcal S}$ d .
