  Let $R$ be a commutative ring, $G$ a group and $RG$ its group ring. Let $\vp
: RG\to RG$ denote the $R$-linear extension of an involution $\vp$ defined on
$G$. An element $x$ in $RG$ is said to be $\vp$-antisymmetric if $\vp (x) =
-x$. A characterization is given of when the $\vp$-antisymmetric elements of
$RG$ commute. This is a completion of earlier work.
