The discovery of the short GRB 090510 has raised considerable attention mainly because it had a bright optical afterglow and it is among the most energetic events detected so far within the entire GRB population. The afterglow was observed with swift/UVOT and swift/XRT and evidence of a jet break around 1.5 ks after the burst has been reported in the literature, implying that after this break the optical and X-ray light curve should fade with the same decay slope. As noted by several authors, the post-break decay slope seen in the UVOT data is much shallower than the steep decay in the X-ray band, pointing to an excess of optical flux at late times. We reduced and analyzed new afterglow light-curve data obtained with the multichannel imager GROND. Based on the densely sampled data set obtained with GROND, we find that the optical afterglow of GRB 090510 did indeed enter a steep decay phase starting around 22 ks after the burst. During this time the GROND optical light curve is achromatic, and its slope is identical to the slope of the X-ray data. In combination with the UVOT data this implies that a second break must have occurred in the optical light curve around 22 ks post burst, which, however, has no obvious counterpart in the X-ray band, contradicting the interpretation that this could be another jet break. The GROND data provide the missing piece of evidence that the optical afterglow of GRB 090510 did follow a post-jet break evolution at late times.