Continuous reconstructions of past variations of the Earth's magnetic field are based mainly on paleomagnetic and cosmogenic 10Be records in marine sediments. In both cases, the recording mechanisms can be affected by environmental processes. Climatic overprints are only partially removed by normalization procedures, so that stacking is used to further remove site‐specific effects. Regionally or globally correlated artifacts, however, cannot be removed by stacking. Here we present a modified approach where geomagnetic records are complemented by environmental proxies representing processes that might affect the field recording mechanism. Geomagnetic and environmental records are jointly processed with principal component analysis to obtain a set of components supposed to represent true variations of the geomagnetic field and climatic overprints, respectively. After discussing the theoretical background of this new approach and its underlying assumptions, a practical example is presented, using a worst‐case scenario based on a single 10Be record from the North Atlantic with strong climatic overprints, covering the last 600 ka. The first two principal components, which represent the modulation of 10Be by global climatic variations and by the geomagnetic field, respectively, explain 66.3% of the signal variance. Comparison of the geomagnetic principal component with global relative paleointensity stacks shows that the original climatic overprint can be reduced by a factor of 2, outperforming a 10Be/9Be stack obtained from two sites with little glacial‐interglacial variability. The proposed method for removing climatic overprints can be applied to multiple sites more efficiently than conventional stacking.