  We propose a new ab initio method designed for the accurate calculation of
effective exchange integrals between atoms with numerous open-shells. This
method applies to ferromagnetic as well as antiferromagnetic exchange, direct
or ligand-mediated exchange. Test calculations on high spin transition metal
oxides such as KNiF3, Ba2CoS3 or YMnO3 exhibit a very good accuracy compared
either to the best ab initio calculations --when those are feasible-- and with
experimental evaluations.
