  Let $X$ be a normal algebraic variety over an algebraically closed field $k$
of characteristic zero. We prove that the K\"{a}hler differential sheaf of $X$
is torsion-free if and only if any regular section of the ideal sheaf of the
first order deformation of $X$ inside $X\times_k X$, defined outside the
singular locus of $X \times_k X$, extends regularly to the singular locus.
