  We study the Hardy-Littlewood maximal operator defined via an unconditional
norm, acting on block decreasing functions. We show that the uncentered maximal
operator maps block decreasing functions of special bounded variation to
functions with integrable distributional derivatives, thus improving their
regularity. In the special case of the maximal operator defined by the
l_infty-norm, that is, by averaging over cubes, the result extends to block
decreasing functions of bounded variation, not necessarily special.
