Let $(M,g)$ be a complete connected noncompact Riemannian manifold with sectional curvature $\operatorname{sec}_g \geq 0$. Let $S \subset M$ be a soul of $M$, and let $p: M \to S$ be the Sharafutdinov retraction associated to $S$. Then $p$ is distance nonincreasing: for every $x,y \in M$,