  Using square bridge position, Akbulut-Ozbagci and later Arikan gave
algorithms both of which construct an explicit compatible open book
decomposition on a closed contact $3$-manifold which results from a contact
$(\pm 1)$-surgery on a Legendrian link in the standard contact $3$-sphere. In
this article, we introduce the ``generalized square bridge position'' for a
Legendrian link in the standard contact $5$-sphere and partially generalize
this result to the dimension five via an algorithm which constructs relative
open book decompositions on relative contact pairs.
