  We develop a framework to describe a wide class of flat-band models, with and
without a translational symmetry, by using "molecular orbitals" introduced in
the prior work (HATSUGAI Y. and MARUYAMA I., \textit{EPL}, \textbf{95}, (2011)
20003). Using the molecular-orbital representation, we shed new light on the
band-touching problem between flat and dispersive bands. We show that the band
touching occurs as a result of collapse, or the linearly dependent nature, of
molecular orbitals. Conversely, we can gap out the flat bands by modulating the
molecular orbitals so that they do not collapse, which provides a simple
prescription to construct models having a finite energy gap between flat bands
and dispersive bands.
