If two positive operators $A$ and $B$ commute, then $A\ \sharp _{\alpha}\ B=A^{1-\alpha}B^{\alpha}$ for all $0\leq \alpha \leq 1$. In this note, we prove a norm inequality for the geometric mean $A\ \sharp_{\alpha}\ B$ and its reverse inequality: Let $A$ and $B$ be positive operators on a Hilbert space such that $0