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Sagittarius A* (Sgr A*) is a strong, compact radio source believed to be powered by a super-massive black hole at the galactic center. Extinction by dust and gas in the galactic plane prevents observing it optically, but its position and proper motion have previously been estimated using radio interferometry. We present new VLBI absolute astrometry measurements of its precise position and proper motion in the frame of the third realization of the International Celestial Reference Frame, ICRF3. The observations used were made at 52 epochs on the VLBA at K-band (24 GHz) between June 2006 and August 2022. We find the proper motion of Sgr A* to be -3.128 $\pm$ 0.042 mas/yr in right ascension and -5.584 $\pm$ 0.075 mas/yr in declination, or 6.400 $\pm$ 0.073 mas/yr at a position angle of 209.26 $\pm$ 0.51 degrees. We also find its J2000 ICRF3 coordinates at the 2015.0 proper motion epoch to be 17$^h$45$^m$40.034047$^s$ $\pm$ 0.000018$^s$, -29$^o$00'28.21601'' $\pm$ 0.00044''. In galactic coordinates, Sgr A* shows proper motion of -6.396 $\pm$ 0.071 mas/yr in galactic longitude and -0.239 $\pm$ 0.045 mas/yr in galactic latitude, indicating solar motion of 248.0 $\pm$ 2.8 km/sec in the galactic plane and 9.3 $\pm$ 1.9 km/sec towards the north galactic pole.