We have considered the expansion of the two-body reduced density matrices (2-RDM) in terms of the two-body cumulant (2-CRDM) which represents pure two-body correlation effects. It possesses also the advantage to be extensive contrarily to the 2-RDM. Thus, the 2-CRDM of a whole system should be well described in a restricted part of the system if one works in a localized basis set of orbitals. We studied the locality of the 2-CRDM, and consequently the correlation energy, for linear chain of hydrogen atoms H-N (N = 6,...,12) at different geometries of their dimerization. Our results are encouraging for developing low computational cost ab initio methods using the 1- and 2-RDM formalism. (C) 2003 Elsevier B.V. All rights reserved.