A new phase-coherent technique for the calibration of polarimetric data is presented. Similar to the one-dimensional form of convolution, data are multiplied by the response function in the frequency domain. Therefore, the system response can be corrected with arbitrarily high spectral resolution, effectively treating the problem of bandwidth depolarization. As well, the original temporal resolution of the data is retained. The method is therefore particularly useful in the study of radio pulsars, in which high time resolution and polarization purity are essential requirements of high-precision timing. As a demonstration of the technique, it is applied to full-polarization baseband recordings of the nearby millisecond pulsar, PSR J0437-4715.