  Whether High Velocity Clouds (HVCs) can form by condensation of the hot ($T
\sim 10^6 \, {\rm K}$) Galactic corona as a consequence of thermal
instabilities has been controversial. Here we re-examine this problem and we
suggest that rotation of the corona might be a missing key ingredient. We do
this by studying the evolution of the models of rotating galactic coronae
presented in Sormani et al. (2018) under the presence of cooling and thermal
conduction. We combine a linear stability analysis with the results of local
and global hydrodynamical simulations. We find that condensations are likely to
occur in regions where the corona has substantial rotational support. Under
reasonably general assumptions on the rotation profile of the corona, the
locations where condensations are expected are in remarkable agreement with the
observed location of the major non-magellanic HVCs complexes in our Galaxy
(namely, at distances $< 15 \, \rm kpc$ from the Sun and within $30^\circ$ from
the disc plane). We conclude that HVCs can form by thermal instabilities
provided that (i) the corona is rotating substantially in the inner ($R < 50 \,
\rm kpc$) parts, as suggested by current observational data and predicted by
cosmological simulations of galaxy formation; (ii) close to the disc the corona
is well-represented by a nearly-equilibrium stratified rotating structure (as
opposed to a fast cooling flow). Our results also suggest that a better
understanding of the disc-halo interface, including supernova feedback, is
critical to understand the origin of HVCs.
