  Let $FG$ be the group algebra of a finite $2$-group $G$ over a finite field
$F$ of characteristic two and $\circledast$ an involution which arises from
$G$. The $\circledast$-unitary subgroup of $FG$, denoted by
$V_{\circledast}(FG)$, is defined to be the set of all normalized units $u$
satisfying the property $u^{\circledast}=u^{-1}$. In this paper we establish
the order of $V_{\circledast}(FG)$ for all involutions $\circledast$ which
arise from $G$, where $G$ is a finite cyclic $2$-group and show that all
$\circledast$-unitary subgroups of $FG$ are not isomorphic.
