We present an algorithm for removing environmental noise from neurophysiological recordings such as magnetoencephalography (MEG). Noise fields measured by reference magnetometers are optimally filtered and subtracted from brain channels. The filters (one per reference/brain sensor pair) are obtained by delaying the reference signals, orthogonalizing them to obtain a basis, projecting the brain sensors onto the noise-derived basis, and removing the projections to obtain clean data. Simulations with synthetic data suggest that distortion of brain signals is minimal. The method surpasses previous methods by synthesizing, for each reference/brain sensor pair, a filter that compensates for convolutive mismatches between sensors. The method enhances the value of data recorded in health and scientific applications by suppressing harmful noise, and reduces the need for deleterious spatial or spectral filtering. It should be applicable to a wider range of physiological recording techniques, such as EEG, local field potentials, etc.