  High-velocity clouds (HVCs) are neutral or ionised gas clouds in the vicinity
of the Milky Way that are characterised by high radial velocities inconsistent
with participation in the regular rotation of the Galactic disc. Previous
attempts to create a homogeneous all-sky HI map of HVCs have been hampered by a
combination of poor angular resolution, limited surface brightness sensitivity
and suboptimal sampling. Here, a new and improved HI map of Galactic HVCs based
on the all-sky HI4PI survey is presented. The new map is fully sampled and
provides significantly better angular resolution (16.2 versus 36 arcmin) and
column density sensitivity (2.3 versus 3.7 * 10^18 cm^-2 at the native
resolution) than the previously available LAB survey. The new HVC map resolves
many of the major HVC complexes in the sky into an intricate network of narrow
HI filaments and clumps that were not previously resolved by the LAB survey.
The resulting sky coverage fraction of high-velocity HI emission above a column
density level of 2 * 10^18 cm^-2 is approximately 15 per cent, which reduces to
about 13 per cent when the Magellanic Clouds and other non-HVC emission are
removed. The differential sky coverage fraction as a function of column density
obeys a truncated power law with an exponent of -0.93 and a turnover point at
about 5 * 10^19 cm^-2. HI column density and velocity maps of the HVC sky are
made publicly available as FITS images for scientific use by the community.
