In this paper we present a method for applying a second-order correction to the polarization data taken at the very large array (VLA). We found that the standard polarization calibration method is inadequate for obtaining a polarization angle time series with position angle constancy better than a few degrees over several hours. Even after application of a more sophisticated ionospheric Faraday rotation model than is commonly employed in VLA polarization measurements, the rms scatter in position angle exceeded 2¿ at 20 cm. In order to reduce this scatter, a polarization ''self-calibration'' method was developed to correct the data for residual instrumental polarization, here noted by the array-averaged instrumental polarization error A to be defined and discussed in section 5, and ionospheric Faraday rotation errors Δ&thgr;FR. Using four extragalactic radio sources with fractional polarization ranging from 1 to 4.8%, the residual errors A and Δ&thgr;FR was estimated. A typical value of A was 10-3 and the magnitude of Δ&thgr;FR was less than 2¿. These residuals, however, are enough to limit the VLA polarization angle measurement to roughly 2¿ at 20 cm. The instrumental polarization error was found to be time variable with a timescale of a few hours. These errors were removed from the data, and the corrected data showed an improvement in polarization time series with a smaller scatter in position angle, except for the source 0010+005. It was close to the Sun on the day of the observation, and we believe the excess fluctuations are due to coronal plasma turbulence. We believe the technique described in this paper will be of use to observations in which the Faraday rotation varies during the course of an observing session, such as measurements of coronal Faraday rotation, or in which it is important to eliminate or minimize the Faraday rotation noise, An example of the latter type of observation would be the study of pulsar rotation measure variations over long time intervals. Of course, a result of this procedure is a precision determination of ionospheric rotation measure, in principle in various directions. Such observations might aid radio remote sensing studies of the ionosphere.