  (abridged) We have measured the absolute proper motions of nine low-latitude,
inner Galaxy globular clusters, namely NGC 6273 (M 19), NGC 6284, NGC 6287, NGC
6293, NGC 6333 (M 9), NGC 6342, NGC 6356, NGC 6388 and NGC 6441. These are the
first determinations ever made for these clusters. The proper motions are on
the ICRS via Hipparcos. The proper-motion errors range between 0.4 and 0.9
mas/yr, and are dominated by the number of measurable cluster members in these
regions which are very crowded by the bulge/bar and the thick disk. This samle
contains five metal poor ([Fe/H < -1.0) and four metal rich clusters; seven
clusters are located within 4 kpc from the Galactic center, while the remaining
two, namely NGC 6356 and NGC 6284 are in the background of the bulge at 7.5 kpc
from the Galactic center. By combining proper motions with radial velocities
and distances from the literature we derive 3D velocities. In a number of
cases, distance uncertainties make the kinematical classification ambiguous.
  The two metal rich clusters NGC 6388 and NGC 6441 have velocities
incompatibile with membership in the thick disk or the bar of the Milky Way.
They can be though of as members of a kinematically hot system in the inner
Galaxy. Curiously, both clusters have similar velocity components. Together
with their similar Galactic location and peculiar but similar
stellar-population characteristics, these two clusters may share a common
origin. Their velocities are also very low indicating that the two clusters are
now at/near apocenter, and they will not leave the inner ~4 kpc of the Galaxy.
