  We have measured the absolute proper motions of four low-latitude,
inner-Galaxy globular clusters. These clusters are: NGC 6266 (M62), NGC 6304,
NGC 6316 and NGC 6723. The proper motions are on the Hipparcos system, as no
background extragalactic objects are found in these high-extinction regions.
The proper-motion uncertainties range between 0.3 and 0.6 mas/yr.
  We discuss the kinematics of these clusters and of three additional bulge
clusters -- NGC 6522, NGC 6528 and NFC 6553 -- whose proper motions with
respect to bulge stars had been determined previously. We find that all of the
clusters have velocities that confine them to the bulge region. Of the three
metal poor clusters ([Fe/H] < -1.0), NGC 6522, and NGC 6723 have kinematics
consistent with halo membership. The third cluster, NGC 6266 however, appears
to belong to a rotationally-supported system. Of the four metal rich clusters
([Fe/H] >= -1.0), NGC 6304 and NGC 6553 also have kinematics consistent with
membership to a rotationally-supported system. NGC 6528 has kinematics,
metallicity and mass that argue in favor of a genuine Milky-Way bar cluster.
NGC 6316's kinematics indicate membership to a hotter system than the bar.
