  To encode an important property of the "no broken circuit bases" of the
Orlik-Solomon-Terao algebras, Andras Szenes has introduced a particular type of
bases, the so called "diagonal basis". We prove that this definition extends
naturally to a large class of algebras, the so called chi-algebras. Our
definitions make also use of an "iterative residue formula" based on the
matroidal operation of contraction. This formula can be seen as the
combinatorial analogue of an iterative residue formula introduced by Szenes. As
an application we deduce nice formulas to express a pure element in a diagonal
basis.
