The inner 10 pc of our Galaxy contains many counterpart candidates of the very high energy (VHE; >100 GeV) γ-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 VHE and beyond and of providing the observed γ-ray flux. Previous attempts to address this source confusion were hampered by the fact that the projected distances between these objects were of the order of the error circle radius of the emission centroid (34 arcsec, 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 γ-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 arcsec per axis. The position of HESS J1745−290 is obtained by fitting a multi-Gaussian profile to the background-subtracted γ-ray count map. A spatial comparison of the best-fitting 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 arcsec, 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 γ-ray emission.