We present a technique for removing global effects from functional magnetic resonance imaging (fMRI) images, using a voxel-level linear model of the global signal (LMGS). The procedure does not assume low-frequency global effects and is based on the assumption that the global signal (the time course of the average intensity per volume) is replicated in the same pattern throughout the brain, although not necessarily at the same magnitude. A second assumption is that all effects that match the global signal are of no interest and can be removed. The method involves modeling the time course of each voxel to the global signal and removing any such global component from the voxel's time course. A challenge that elicits a large change in the global blood oxygenation level-dependent (BOLD) signal, inspired hypercapnia (5% CO(2)/95% O(2)), was administered to 14 subjects during a 144-s, 24-scan fMRI procedure; baseline series were also collected. The method was applied to these data and compared to intensity normalization and low-frequency spline detrending. A large global BOLD signal increase emerged to the hypercapnic challenge. Intensity normalization failed to remove global components due to regional variability. Both LMGS and spline detrending effectively removed low-frequency components, but unlike spline detrending (which is designed to remove only low frequency trends), the LMGS removed higher-frequency global fluctuations throughout the challenge and baseline series. LMGS removes all effects correlated with the global signal, and may be especially useful for fMRI data that include large global effects and for generating detrended images to use with subsequent volume-of-interest (VOI) analyses.