  Recent precise determinations of the primordial He-abundance (Y_p) from
cosmic microwave background (CMB) analyses and cosmological nucleosynthesis
computations, provide Y_p=0.248$\pm$0.001. On the other hand, recent works on
the initial He-abundance of Galactic globular cluster (GGC) stars, making use
of the R parameter as He-indicator, have consistently obtained
$Y_{GGC}\sim$0.20.
  In light of this serious discrepancy that casts doubt on the adequacy of low
mass He-burning stellar models, we have rederived the initial He-abundance for
stars in two large samples of GGCs, by employing theoretical models computed
using new and more accurate determinations of the Equation of State for the
stellar matter, and of the uncertain $^{12}$C$(\alpha,\gamma)^{16}$O reaction
rate. Our models include semiconvection during the central convective
He-burning phase, while the breathing pulses are suppressed, in agreement with
the observational constraints coming from the measurements of the R_2 parameter
in a sample of clusters. By taking into account the observational errors on the
individual R-parameter values, as well as uncertainties in the GGC [Fe/H]
scale, treatment of convection and $^{12}$C$(\alpha,\gamma)^{16}$O reaction
rate, we have obtained, respectively, a mean $Y_{GGC}$=0.243$\pm$0.006 and
$Y_{GGC}$=0.244$\pm$0.006 for the two studied GGC samples. These estimates are
now fully consistent with Y_p obtained from CMB studies. Moreover, the trend of
the individual He-abundances with respect to [Fe/H] is consistent with no
appreciable He-enrichment along the GGC metallicity range.
