Convolving a finite-impulse-response (FIR) filter with a magnetic anomaly map produces a reduction-to-the-pole (RTP) that is superior to that of the conventional Fourier-transform approach. The conventional approach, in which the map's Fourier transform is multiplied by the frequency response of the RTP filter, is flawed by not accounting properly for the dimensions of the respective Fourier transforms. The resultant wraparound effect of circular convolution degrades the RTP map. The FIR filter, combined with linear convolution and appropriate choices for dimensions of data and filter, eliminates the wraparound effect, minimizes contamination of the result by noise, and improves stability. These properties are illustrated by a synthetic example and by application to an actual data set.