  We show that a function $ f $ of bounded variation satisfies $$ \Var Mf \leq
C \Var f $$ where $ Mf $ is the centered Hardy-Littlewood maximal function of $
f $. Consequently, the operator $ f \mapsto (Mf)' $ is bounded from $
W^{1,1}(R) $ to $ L^{1}(R) $. This answers a question of Hajlasz and Onninen in
the one-dimensional case.
