  The note concerns the $\bar\partial$ problem on product domains in $\mathbb
C^2$. We show that there exists a bounded solution operator from $C^{k,
\alpha}$ into itself, $k\in \mathbb Z^+\cup \{0\}, 0<\alpha< 1$. The regularity
result is optimal in view of an example of Stein-Kerzman.
