  We find new families of solutions of the $D_{n+1}^{(2)}$ boundary Yang-Baxter
equation. The open spin-chain transfer matrices constructed with these
K-matrices have quantum group symmetry corresponding to removing one node from
the $D_{n+1}^{(2)}$ Dynkin diagram, namely, $U_{q}(B_{n-p}) \otimes
U_{q}(B_{p})$, where $p=0, \ldots, n$. These transfer matrices also have a $p
\leftrightarrow n-p$ duality symmetry. These symmetries help to account for the
degeneracies in the spectrum of the transfer matrix.
