About 4 ^ { \prime \prime } south of the young A0-type star HR 7329 , a faint companion candidate was found by Lowrance et al . ( 2000 ) . Its spectral type of M7-8 is consistent with a young brown dwarf companion . Here , we report ten new astrometric imaging observations of the pair HR 7329 A and B , obtained with the Hubble Space Telescope and the Very Large Telescope , aimed at showing common proper motion with high significance and possible orbital motion of B around A . With 11 yrs of epoch difference between the first and our last image , we can reject by more than 21 \sigma that B would be a non-moving background object unrelated to A . We detect no change in position angle and small or no change in separation ( 2.91 \pm 2.41 mas/yr ) , so that the orbit of HR 7329 B around A is inclined and/or eccentric and/or the orbital motion is currently only in radial direction . If HR 7329 B is responsible for the outer radius of the debris disk around HR 7329 A being 24 AU , and if HR 7329 B currently is at its apastron at 200 AU ( 4.2 ^ { \prime \prime } at 47.7 pc ) , we determine its pericenter distance to be 71 AU , its semi-major axis to be 136 AU , and its eccentricity to be e = 0.47 . From the magnitude differences between HR 7329 A and B and the 2MASS magnitudes for the HR 7329 A+B system , we can estimate the magnitudes of HR 7329 B ( J= 12.06 \pm 0.19 , H= 11.75 \pm 0.10 , K _ { s } = 11.6 \pm 0.1 , L= 11.1 \pm 0.2 mag ) and then , with a few otherwise known parameters , its luminosity and mass ( 20-50 Jupiter masses ) . In the deepest images available , we did not detect any additional companion candidates up to \leq 9 ^ { \prime \prime } , but determine upper limits in the planetary mass regime .