  We study an optimal transport problem with a backward martingale constraint
in a pseudo-Euclidean space $S$. We show that the dual problem consists in the
minimization of the expected values of the Fitzpatrick functions associated
with maximal $S$-monotone sets. An optimal plan $\gamma$ and an optimal maximal
$S$-monotone set $G$ are characterized by the condition that the support of
$\gamma$ is contained in the graph of the $S$-projection on $G$. For a Gaussian
random variable $Y$, we get a unique decomposition: $Y = X+Z$, where $X$ and
$Z$ are independent Gaussian random variables taking values, respectively, in
complementary positive and negative linear subspaces of the $S$-space.
