Lithium abundances in a selected sample of halo stars have been revised by using the new accurate infrared flux method (IRFM) effective temperatures by Alonso, Arribas & Martinez-Roger. From 41 plateau stars (T-eff > 5700 and [Fe/H] less than or equal to - 1.5) we found no evidence for intrinsic dispersion, a tiny trend with T-eff and no trend with [Fe/H]. The trend with the T-eff is fully consistent with the standard Li isochrones of Deliyannis, Demarque & Kawaler, implying a primordial value for Li of A(Li) = 2.238 +/- 0.012(1 sigma) +/- 0.05(sys). The present results argue against any kind of depletion predicted by diffusion, rotational mixing or stellar winds. Therefore the Li observed in Population II stars provides a direct and reliable estimate of the baryonic density which can rival other baryonic indicators such as the deuterium in high-redshift systems. The present upwards revision of primordial Li in the framework of standard big bang nucleosynthesis (SBBN) gives, at 1 sigma, two solutions for the baryonic density: Omega(B)h(2) = 0.0062(-0.0011)(+0.0018) or Omega(B)h(2) = 0.0146(-0.0033)(+0.0029).