The huge amount of data acquired by Mars Global Surveyor during its mapping period provides a unique opportunity to reassess the paleomagnetic pole positions of Mars previously determined on the basis of the limited low-altitude magnetic data. We identify nine small and isolated magnetic anomalies on the basis of the global magnetic maps and model each anomaly using a vertical prism of elliptical cross section. Both high-altitude (360--430 km) and low-altitude (100--200 km) magnetic data are used simultaneously. We calculate a paleomagnetic pole position assuming that the body is magnetized by a dipole core field. Although the new pole positions do not cluster as closely as the old ones, the new cluster overlaps the older cluster. The clustering suggests that Mars' rotation axis has likely wandered by ~50¿--60¿ in the last ~4 Gyr. The number of north and south poles in the cluster suggests at least one reversal of the core field during the time the source bodies acquired magnetization.