We present improved relative astrometry for stars within the central half parsec of our Galactic Center (GC) based on data obtained with the 10 m W. M. Keck Observatory from 1995 to 2017. The new methods used to improve the astrometric precision and accuracy include correcting for local astrometric distortions, applying a magnitude-dependent additive error, and more carefully removing instances of stellar confusion. Additionally, we adopt jackknife methods to calculate velocity and acceleration uncertainties. The resulting median proper motion uncertainty is 0.05 mas yr -1 for our complete sample of 1184 stars in the central 10″ (0.4 pc). We have detected 24 accelerating sources, 2.6 times more than the number of previously published accelerating sources, which extend out to 4″ (0.16 pc) from the black hole. Based on S0-2's orbit, our new astrometric analysis has reduced the systematic error of the supermassive black hole (SMBH) by a factor of 2. The linear drift in our astrometric reference frame is also reduced in the north-south direction by a factor of 4. We also find the first potential astrometric binary candidate S0-27 in the GC. These astrometric improvements provide a foundation for future studies of the origin and dynamics of the young stars around the SMBH, the structure and dynamics of the old nuclear star cluster, the SMBH's properties derived from orbits, and tests of general relativity in a strong gravitational field.