In this paper we present a new , accurate determination of the three components of the absolute space velocity of the Galactic globular cluster NGC 6397 ( l \simeq 338 ^ { \circ } , b \simeq - 12 ^ { \circ } ) . 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 } ) _ { J 2000.0 } = ( +3.39 \pm 0.15 , -17.55 \pm 0.15 ) mas yr ^ { -1 } , and V _ { rad } = +18.36 \pm 0.09 ( \pm 0.10 ) km s ^ { -1 } . Assuming a Galactic potential , we calculate the cluster orbit for various assumed distances , and briefly discuss the implications .