The purpose of this paper is to provide new information about the structure of orthosymmetric bilinear operators and, in particular, to prove a Radon–Nikod'ym type theorem for this class of operators. The main tools used and developed in the paper are based on homogeneous functional calculus on vector lattices and squares of vector lattices. Therefore, some useful facts concerning an interplay between squares of vector lattices and homogeneous functional calculus are collected.