  Despite the efforts of the past decade, the origin of the bimodal
horizontal-branch (HB) found in some globular clusters (GCs) remains a
conundrum. Inspired by the discovery of multiple stellar populations in the
{\it most massive} Galactic GC, $\omega$ Centauri, we investigate the
possibility that two distinct populations may coexist and are responsible for
the bimodal HBs in the {\it third} and {\it fifth} brightest GCs, NGC 6388 and
NGC 6441. Using the population synthesis technique, we examine two different
chemical ``self-enrichment'' hypotheses in which a primordial GC was
sufficiently massive to contain two or more distinct populations as suggested
by the populations found in $\omega$ Cen: (1) the age-metallicity relation
scenario in which two populations with different metallicity and age coexist,
following an internal age-metallicity relation, and (2) the super-helium-rich
scenario in which GCs contain a certain fraction of helium-enhanced stars, for
instance, the second generation stars formed from the helium-enriched ejecta of
the first. The comparative study indicates that the detailed color-magnitude
diagram morphologies and the properties of the RR Lyrae variables in NGC 6388
and NGC 6441 support the latter scenario; i.e., the model which assumes a minor
fraction ($\sim$ 15 %) of helium-excess (Y $\simeq$ 0.3) stars. The results
suggest that helium content is the main driver behind the HB bimodality found
most often in massive GCs. If confirmed, the GC-to-GC variation of helium
abundance should be considered a {\it local} effect, further supporting the
argument that age is the {\it global} second parameter of HB morphology.
