  We re-examine the big bang nucleosynthesis (BBN) bounds on the mixing of
neutrinos with sterile species. These bounds depend on the assumption that the
relic neutrino asymmetry $L_{\nu}$ is very small. We show that for $L_{\nu}$
large enough (greater than about $10^{-5}$) the standard BBN bounds do not
apply. We apply this result to the sterile neutrino solution to the atmospheric
neutrino anomaly and show that for $L_{\nu} > 7 \times 10^{-5}$ it is
consistent with BBN. The BBN bounds on sterile neutrinos mixing with electron
neutrinos can also be weakened considerably.
