  The dichromatic number of $D$, denoted by $\overrightarrow{\chi}(D)$, is the
smallest integer $k$ such that $D$ admits an acyclic $k$-coloring. We use
$mader_{\overrightarrow{\chi}}(F)$ to denote the smallest integer $k$ such that
if $\overrightarrow{\chi}(D)\ge k$, then $D$ contains a subdivision of $F$. A
digraph $F$ is called Mader-perfect if for every subdigraph $F'$ of $F$, ${\rm
mader }_{\overrightarrow{\chi}}(F')=|V(F')|$. We extend octi digraphs to a
larger class of digraphs and prove that it is Mader-perfect, which generalizes
a result of Gishboliner, Steiner and Szab\'{o} [Dichromatic number and forced
subdivisions, {\it J. Comb. Theory, Ser. B} {\bf 153} (2022) 1--30]. We also
show that if $K$ is a proper subdigraph of $\overleftrightarrow{C_4}$ except
for the digraph obtained from $\overleftrightarrow{C_4}$ by deleting an
arbitrary arc, then $K$ is Mader-perfect.
