Let $\cal D $ denote the collection of dyadicintervals in the unit interval. Let $\tau$ be a rearrangement of the dyadic intervals. We study theinduced operator

$$ Th_I = h_{\tau(I)}$$

where $h_I$ is the $L^{\infty}$ normalizedHaar function. We find geometric conditions on $\tau$ which are necessary and sufficient for $T$ to bebounded on $BMO$. We also characterize the rearrangements of the $L^p$ normalized Haar system in$L^p.$

1991 Mathematics Subject Classification: 42C20, 43A17, 47B38.