  Let $(X,\mathcal{A}, \mu)$ be a probability measure space and let $T_i,$
$1\leq i\leq H,$ be invertible bi measurable measure preserving transformations
on this measure space. We give a sufficient condition for the product of $H$
bounded functions $f_1, f_2, ..., f_H$ to be a coboundary. This condition turns
out to be also necessary when one seeks bounded coboundaries.
