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We consider the space of binary forms of degree $n\ge 1$ denoted by $R_n:=ℂ[x,y{]}_n$. We will show that every polynomial automorphism of $R_n$ which commutes with the linear ${\mathrm{SL}}_2\left(ℂ\right)$-action and which maps the variety of forms with pairwise distinct zeroes into itself, is a multiple of the identity on $R_n$.