  Prompted by the level of accuracy now being achieved in tests of the
unitarity of the CKM matrix, we consider the possible modification of the Fermi
matrix element for the $\beta$-decay of a neutron, including possible in-medium
and isospin violating corrections. While the nuclear modifications lead to very
small corrections once the Behrends-Sirlin-Ademollo-Gatto theorem is respected,
the effect of the $u-d$ mass difference on the conclusion concerning $V_{ud}$
is no longer insignificant. Indeed, we suggest that the correction to the value
of $|V_{ud}|^2 \, + \, |V_{us}|^2 \, + \, |V_{ub}|^2$ is at the level of
$10^{-4}$.
