  Let $R$ be a ring with $char(R)\neq2$ whose unit group are denoted by
$\mathcal{U}(R)$, $G$ a group, and $RG$ its group ring. Let $*$ be an
involution in $G$, $\sigma:G\rightarrow\mathcal{U}(R)$ be a nontrivial group
homomorphism, with $ker\ \sigma=N$, satisfying $xx^*\in N$ for all $x\in G$,
and define the generalized oriented involution $\sigma*$ in $RG$ by $\left(
\sum_{x\in G}\alpha_xx\right)^{\sigma*}=\sum_{x\in G}\sigma(x)\alpha_xx^*$. An
element $\alpha\in RG$ is called skew-symmetric if $\alpha^{\sigma *}=-\alpha$,
and the set of all skew-symmetric elements are denoted by $(RG)^-$. In this
paper, we will classify the group rings $RG$ such that $(RG)^-$ is
anticommutative, generalizing, and obtaining as consequence, the main result of
\cite{GP13a}.
