We present a calibration of the absolute pointing accuracy of the Advanced Satellite for Cosmology and Astrophysics (ASCA) which allows us to compensate for a large error (up to 1') in the derived source coordinates. We parameterize a temperature dependent deviation of the attitude solution which is responsible for this error. By analyzing ASCA coordinates of 100 bright active galactic nuclei, we show that it is possible to reduce the uncertainty in the sky position for any given observation by a factor of 4. The revised 90% error circle radius is then 12'', consistent with preflight specifications, effectively restoring the full ASCA pointing accuracy. Herein, we derive an algorithm which compensates for this attitude error and present an internet-based table to be used to correct post facto the coordinate of all ASCA observations. While the above error circle is strictly applicable to data taken with the on-board Solid-state Imaging Spectrometers (SISs), similar coordinate corrections are derived for data obtained with the Gas Imaging Spectrometers (GISs), which, however, have additional instrumental uncertainties. The 90% error circle radius for the central 20' diameter of the GIS is 24''. The large reduction in the error circle area for the two instruments offers the opportunity to greatly enhance the search for X-ray counterparts at other wavelengths. This has important implications for current and future ASCA source catalogs and surveys.