  The Milky Way halo is one of the few galactic haloes that provides a unique
insight into galaxy formation by resolved stellar populations. Here, we present
a catalogue of $\sim$47 million halo stars selected independent of parallax and
line-of-sight velocities, using a combination of Gaia DR3 proper motion and
photometry by means of their reduced proper motion. We select high tangential
velocity (halo) main sequence stars and fit distances to them using their
simple colour-absolute-magnitude relation. This sample reaches out to $\sim$21
kpc with a median distance of $6.6$ kpc thereby probing much further out than
would be possible using reliable Gaia parallaxes. The typical uncertainty in
their distances is $0.57_{-0.26}^{+0.56}$ kpc. Using the colour range
$0.45<(G_0-G_\mathrm{RP,0})<0.715$ where the main sequence is narrower, gives
an even better accuracy down to $0.39_{-0.12}^{+0.18}$ kpc in distance. The
median velocity uncertainty for stars within this colour range is 15.5 km/s.
The distribution of these sources in the sky, together with their tangential
component velocities, are very well-suited to study retrograde substructures.
We explore the selection of two complex retrograde streams: GD-1 and Jhelum.
For these streams, we resolve the gaps, wiggles and density breaks reported in
the literature more clearly. We also illustrate the effect of the kinematic
selection bias towards high proper motion stars and incompleteness at larger
distances due to Gaia's scanning law. These examples showcase how the full RPM
catalogue made available here can help us paint a more detailed picture of the
build-up of the Milky Way halo.
