  In this paper we present a new, accurate determination of the three
components of the absolute space velocity of the Galactic globular cluster
NGC6397 (l 338d, b -12d). We used three HST/WFPC2 fields with multi-epoch
observations to obtain astrometric measurements of objects in three different
fields in this cluster. The identification of 33 background galaxies with sharp
nuclei allowed us to determine an absolute reference point and measure the
absolute proper motion of the cluster. The third component has been obtained
from radial velocities measured on spectra from the multi-fiber spectrograph
FLAMES at UT2-VLT. We find [mu_alpha cos(delta), mu_delta](J2000.0) = [+3.39
+/- 0.15, -17.55 +/- 0.15] mas/yr, and V_rad = +18.36 +/- 0.09 (+/-0.10) km/s.
Assuming a Galactic potential, we calculate the cluster orbit for various
assumed distances, and briefly discuss the implications.
