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We present improved relative astrometry for stars within the central halfparsec of our Galactic Center based on data obtained with the 10 m W. M. KeckObservatory from 1995 to 2017. The new methods used to improve the astrometricprecision and accuracy include correcting for local astrometric distortions,applying a magnitude dependent additive error, and more carefully removinginstances of stellar confusion. Additionally, we adopt jackknife methods tocalculate velocity and acceleration uncertainties. The resulting median propermotion uncertainty is 0.05 mas/yr for our complete sample of 1184 stars in thecentral 10'' (0.4 pc). We have detected 24 accelerating sources, 2.6 times morethan the number of previously published accelerating sources, which extend outto 4'' (0.16 pc) from the black hole. Based on S0-2's orbit, our newastrometric analysis has reduced the systematic error of the supermassive blackhole (SMBH) by a factor of 2. The linear drift in our astrometric referenceframe is also reduced in the North-South direction by a factor of 4. We alsofind the first potential astrometric binary candidate S0-27 in the Galacticcenter. These astrometric improvements provide a foundation for future studiesof the origin and dynamics of the young stars around the SMBH, the structureand dynamics of the old nuclear star cluster, the SMBH's properties derivedfrom orbits, and tests of General Relativity (GR) in a strong gravitationalfield.

The Galactic Center: Improved Relative Astrometry for Velocities, Accelerations, and Orbits near the Supermassive Black Hole