Automorphisms of certain affine complements in projective space

We prove that every biregular automorphism of the affine algebraic variety ${\mathbb P}^M\setminus S$, $M\geqslant 3$, where $S\subset {\mathbb P}^M$ is a hypersurface of degree $m\geqslant M+1$ with a unique singular point of multiplicity $(m-1)$, resolved by one blow up, is a restriction of some automorphism of the projective space ${\mathbb P}^M$ preserving the hypersurface $S$; in particular, for a general hypersurface $S$ the group $\operatorname{Aut}({\mathbb P}^M\setminus S)$ is trivial.
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