A remark on Gersten complex for Milnor $K$-theory

In this note, we consider the Gersten complex for Milnor $K$-theory over a regular local Henselian domain $S$ and prove that in degrees $\geq \dim S\geq 1$,theGerstencomplexofanessentiallysmoothHenselianlocal$S$-scheme is exact.