  For a family of height one orders $(X,\le)$ and each non-degenerate solution
$r_0\colon X\times X\longrightarrow X\times X$ of the set-theoretic braid
equation on $X$ satisfying suitable conditions, we obtain all the
non-degenerate solutions of the braid equation on the incidence coalgebra of
$(X,\le)$ that extend $r_0$.
