  We derive a simple prescription for including beyond-linear halo bias within
the standard, analytical halo-model power spectrum calculation. This results in
a corrective term that is added to the usual two-halo term. We measure this
correction using data from $N$-body simulations and demonstrate that it can
boost power in the two-halo term by a factor of $\sim2$ at scales $k\sim0.7\,h
Mpc^{-1}$, with the exact magnitude of the boost determined by the specific
pair of fields in the two-point function. How this translates to the full power
spectrum depends on the relative strength of the one-halo term, which can mask
the importance of this correction to a greater or lesser degree, again
depending on the fields. Generally we find that our correction is more
important for signals that arise from lower-mass haloes. When comparing our
calculation to simulated data we find that the under-prediction of power in the
transition region between the two- and one-halo terms, which typically plagues
halo-model calculations, is almost completely eliminated when including the
full non-linear halo bias. We show improved results for the auto and cross
spectra of galaxies, haloes and matter. In the specific case of matter-matter
or matter-halo power we note that a large fraction of the improvement comes
from the non-linear biasing between low- and high-mass haloes. We envisage our
model being useful in the analytical modelling of cross correlation signals.
Our non-linear bias halo-model code is available at
https://github.com/alexander-mead/BNL
