# Codimension of the non-locally free locus

Let $X$ be a Noetherian, integral scheme. Let $\mathcal{F}$ be a torsion free sheaf on $X$ and let $U \subseteq X$ be the open subscheme where $\mathcal{F}$ is locally free.

Q. Is it true that $\mathrm{codim}_X(X\setminus U)\geq 2$?

The answer is yes, assuming $X$ to be normal.