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An invertible linear map $\varphi$ on a Lie algebra $L$ is called a triple automorphism of it if $\varphi \left(\right[x,[y,z]\left]\right)=\left[\varphi \right(x),[\varphi \left(y\right),\varphi \left(z\right)\left]\right]$ for $\forall x,y,z\in L$. Let $𝔤$ be a finite-dimensional simple Lie algebra of rank $l$ defined over an algebraically closed field $F$ of characteristic zero, $𝔭$ an arbitrary parabolic subalgebra of $𝔤$. It is shown in this paper that an invertible linear map $\varphi$ on $𝔭$ is a triple automorphism if and only if either $\varphi$ itself is an automorphism of $𝔭$ or it is the composition of an automorphism of $𝔭$ and an extremal map of order $2$.