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Subject head movements are one of the main practical difficulties with brain functional MRI. A fast, accurate method for rotating and shifting a three‐dimensional (3D) image using a shear factorization of the rotation matrix is described. Combined with gradient descent (repeated linearization) on a least squares objective function, 3D image realignment for small movements can be computed as rapidly as whole brain images can be acquired on current scanners. Magn Reson Med 42:1014–1018, 1999. © 1999 Wiley‐Liss, Inc.