  The inner 10 pc of our galaxy contains many counterpart candidates of the
very high energy (VHE; > 100 GeV) gamma-ray point source HESS J1745-290. Within
the point spread function of the H.E.S.S. measurement, at least three objects
are capable of accelerating particles to very high energies and beyond, and of
providing the observed gamma-ray flux. Previous attempts to address this source
confusion were hampered by the fact that the projected distances between those
objects were of the order of the error circle radius of the emission centroid
(34", dominated by the pointing uncertainty of the H.E.S.S. instrument). Here
we present H.E.S.S. data of the Galactic Centre region, recorded with an
improved control of the instrument pointing compared to H.E.S.S. standard
pointing procedures. Stars observed during gamma-ray observations by optical
guiding cameras mounted on each H.E.S.S. telescope are used for off-line
pointing calibration, thereby decreasing the systematic pointing uncertainties
from 20" to 6" per axis. The position of HESS J1745-290 is obtained by fitting
a multi-Gaussian profile to the background-subtracted gamma-ray count map. A
spatial comparison of the best-fit position of HESS J1745-290 with the position
and morphology of candidate counterparts is performed. The position is, within
a total error circle radius of 13", coincident with the position of the
supermassive black hole Sgr A* and the recently discovered pulsar wind nebula
candidate G359.95-0.04. It is significantly displaced from the centroid of the
supernova remnant Sgr A East, excluding this object with high probability as
the dominant source of the VHE gamma-ray emission.
