  Vasiliev system of higher-spin equations contains a free complex parameter
$\eta$. Solving the generating system order by order one obtains physical
vertices proportional to various powers of $\eta$ and $\bar{\eta}$. Recently
$\eta^2$ and $\bar{\eta}^2$ vertices in the field equations for zero-form field
were written in the $Z$-dominated form implying their spin-locality by virtue
of $Z$-dominance Lemma. Here we obtain explicit $Z$-independent spin-local form
for the vertex $\Upsilon^{\eta\eta}_{\omega CCC}$ for its $\omega CCC$-ordered
part where $\omega$ and $C$ denote gauge one-form and field strength zero-form
higher-spin fields valued in arbitrary associative algebra in which case the
order of product factors in $\omega CCC$ matters.
