We present the Keplerian orbit of S62 around the supermassive black hole Sagittarius A* (SgrA*) in the center of our Galaxy. We monitor this S-star cluster member over more than a full orbit around SgrA* using the Very Large Telescope with the near-infrared instruments Spectrograph for INtegral Field Observations in the Near Infrared (SINFONI) and NAOS+CONICA (NACO). For that, we are deriving positional information from deconvolved images. We apply the Lucy-Richardson algorithm to the data sets. The NACO observations cover data from 2002 to 2018, and the SINFONI data cover 2008-2012. S62 can be traced reliably in both data sets. Additionally, we adapt one KECK data point for 2019 that supports the reidentification of S62 after the pericenter passage of S2. With tperiod=9.9yr and a periapse velocity of approximately 10% of the speed of light, S62 has the shortest known stable orbit around the supermassive black hole in the center of our Galaxy to date. From the analysis, we also derive the enclosed mass from a maximum likelihood method to be 4.15 ± 0.6 x 106M☉.