  In [6], the authors construct a cochain complex
$C\!H^*(\mathcal{Z}_{\mathcal{K}})$ on the cohomology of a moment-angle complex
$\mathcal{Z}_{\mathcal{K}}$ and call the resulting cohomology the double
cohomology, $H\!H^*(\mathcal{Z}_{\mathcal{K}})$. In this paper, we study the
change of rank in double cohomology after gluing an $n$-simplex to a simplicial
complex $\mathcal{K}$ in certain conditions. As an application, we give a
positive answer to an open problem in [6]: For any even integer $r$, there
always exists a simlicial complex $\mathcal{K}$ such that $\operatorname{rank}
H\!H^*(\mathcal{Z}_{\mathcal{K}})=r$.
