  The strength of the H$\beta$ index has been computed for the integrated
spectra of model globular clusters from the evolutionary population synthesis.
These models take into account, for the first time, the detailed systematic
variation of horizontal-branch (HB) morphology with age and metallicity. Our
models show that the H$\beta$ index is significantly affected by the presence
of blue HB stars. Because of the contribution from blue HB stars, the H$\beta$
does not monotonically decrease as metallicity increases at a given age.
Instead, it reaches a maximum strength when the distribution of HB stars is
centered around 9500 K, the temperature where the H$\beta$ index becomes
strongest. Our models indicate that the strength of the H$\beta$ index
increases as much as 0.75 {\AA} due to the presence of blue HB stars.
  The comparison of the recent Keck observations of the globular cluster system
in the Milky Way Galaxy with those in giant elliptical galaxies, NGC 1399 and
M87, shows a systematic shift in the H$\beta$ against metallicity plane. Our
models suggest that this systematic difference is understood if the globular
cluster systems in giant elliptical galaxies are several billion years older,
in the mean, than the Galactic counterpart. Further observations of globular
cluster systems in the external galaxies from the large ground-based telescopes
and space UV facilities will enable to clarify whether this difference is
indeed due to the age difference or other explanations are also possible.
