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.