  In this paper, we present the structure of the group of *-unitary units in
the group algebra $FD_{2p}$, where $F$ is a finite field of characteristic $p >
2$, $D_{2p}$ is the dihedral group of order $2p$, and * is the canonical
involution of the group algebra $FD_{2p}$. We also provide the structure of the
maximal $p$-subgroup of the unit group $\mathscr{U}(FD_{2p})$ and compute a
basis of its center.
