Let $U\subset{{\bf R}}^{n}$ be a convex open domain in ${{\bf R}}^{n}$ equipped with the standard affine coordinates $(x_{1},...,x_{n})$, and $K:U\to{{\bf R}}$ be a convex function satisfying the Monge-Ampère equation. Then the Legendre transform $\widehat{K}(y_{1},...,y_{n})=max_{x\in U}(\sum_{i}x_{i}y_{i}-K(x_{1},...,x_{n}))$ also satisfies the Monge-Ampère equation.