A recent publication [1] highlighted the importance of higher order reduced density matrices in obtaining real space chemical indices. In this presentation, I will propose an alternative algorithm to efficiently obtain the first- and second-order RDMs from Slater-determinant expansions. [1] E. Francisco, A. Martín Pendás, M. García-Revilla,and R. Álvarez Boto. A hierarchy of chemical bonding indices in real space from reduced density matrices and cumulants. Computational and Theoretical Chemistry, accepted 14/09/2012