  In this paper, we mainly study the hyponormality of dual Toeplitz operators
on the orthogonal complement of the harmonic Bergman space. First we show that
the dual Toeplitz operator with bounded symbol is hyponormal if and only if it
is normal. Then we obtain a necessary and sufficient condition for the dual
Toeplitz operator $S_\varphi$ with the symbol $\varphi(z) =
az^{n_1}\overline{z}^{m_1} + bz^{n_2} \overline{z}^{m_2}$, $(n_1,n_2,m_1,m_2\in
\mathbb {N}$ and $a,b \in \mathbb{C})$ to be hyponormal. Finally, we show that
the rank of the commutator of two dual Toeplitz operators must be an even
number if the commutator has a finite rank.
