  We present an updated calculation of the uncertainties on the atmospheric
muon-neutrino flux arising from cosmic-ray primaries. For the first time, we
include recent measurements of the cosmic-ray primaries collected since 2005.
We apply a statistical technique that allows the determination of correlations
between the parameters of the GSHL primary-flux parametrisation and the
incorporation of these correlations into the uncertainty on the muon-neutrino
flux. We obtain an uncertainty related to the primary cosmic rays of around
$(5\text{--}15)\%$, depending on energy, which is about a factor of two smaller
than the previously determined uncertainty. The hadron production uncertainty
is added in quadrature to obtain the total uncertainty on the neutrino flux,
which is reduced by $\approx 5\%$. To take into account an unexpected hardening
of the spectrum of primaries above energies of $100$ $\text{GeV}$ observed in
recent measurements, we propose an alternative parametrisation and discuss its
impact on the neutrino flux uncertainties.
