We consider the special case of a series of the form $f = I + F, F \in O_2$. We denote $G := f^\dagger - I, G \in O_2$. Show that $[G]_{d+1} + F \circ (I + [G]_d) \in O_{d+2}$ for all $d \geqslant 1$ (the notation $[f]_d$ is defined in the introduction to the subject).