Two recent papers (Ghez et al. 2008ApJ...689.1044G; Gillessen et al. 2009ApJ...692.1075G) have estimated the mass of and the distance to the massive black hole (MBH) in the center of the Milky Way using stellar orbits. The two astrometric data sets are independent and yielded consistent results, even though the measured positions do not match when simply overplotting the two sets. In this Letter, we show that the two sets can be brought to excellent agreement with each other when we allow for a small offset in the definition of the reference frame of the two data sets. The required offsets in the coordinates and velocities of the origin of the reference frames are consistent with the uncertainties given in Ghez et al. The so-combined data set allows for a moderate improvement of the statistical errors of the mass of and the distance to Sgr A*, but the overall accuracies of these numbers are dominated by systematic errors and the long-term calibration of the reference frame.