  Prediction of the primordial abundances of elements in the big-bang
nucleosynthesis (BBN) is one of the three strong evidences for the big bang
model. Precise knowledge of the baryon-to-photon ratio of the Universe from
observations of the anisotropies of cosmic microwave background radiation has
made the Standard BBN a parameter-free theory. Although, there is a good
agreement over a range of nine orders of magnitude between abundances of light
elements deduced from observations and calculated in primordial
nucleosynthesis, there remains a yet-unexplained discrepancy of $^7$Li
abundance higher by a factor of $\sim 3$ when calculated theoretically. The
primordial abundances depend on the astrophysical nuclear reaction rates and on
three additional parameters, the number of light neutrino flavours, the neutron
lifetime and the baryon-to-photon ratio in the universe. The effect of the
modification of thirty-five reaction rates on light element abundance yields in
BBN was investigated earlier by us. In the present work we have incorporated
the most recent values of neutron lifetime and the baryon-to-photon ratio and
further modified $^3$He($^4$He,$\gamma$)$^7$Be reaction rate which is used
directly for estimating the formation of $^7$Li as a result of $\beta^+$ decay
as well as the reaction rates for t($^4$He,$\gamma$)$^7$Li and
d($^4$He,$\gamma$)$^6$Li. We find that these modifications reduce the
theoretically calculated abundance of $^7$Li by $\sim 12\%$.
