  We provide a new projective condition for a stationary real random field
indexed by the lattice $\Z^d$ to be well approximated by an orthomartingale in
the sense of Cairoli (1969). Ourmain result can be viewed as a multidimensional
version of the martingale-coboundary decomposition method which the idea goes
back to Gordin (1969). It is a powerfull tool for proving limit theorems or
large deviations inequalities for stationary random fields when the
corresponding result is valid for orthomartingales.
