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In this paper, we mainly study the hyponormality of dual Toeplitz operatorson the orthogonal complement of the harmonic Bergman space. First we show thatthe dual Toeplitz operator with bounded symbol is hyponormal if and only if itis normal. Then we obtain a necessary and sufficient condition for the dualToeplitz 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 thatthe rank of the commutator of two dual Toeplitz operators must be an evennumber if the commutator has a finite rank.

Hyponormal dual Toeplitz operators on the orthogonal complement of the Harmonic Bergman space