The energy of a system which is described by a Hamiltonian which includes at most two-particle interactions can be expressed in terms of the second order reduced density matrix. However. for the 2-matrix to have proper symmetry is a weaker condition than requiring that the wavefunction be antisymmetric, which is called the N-representability problem, a problem of long term interest. Coleman [Reduced Density Matrices: Coulson's Challenge, Springer, New York, 2000] however, proposed an algorithm which ensures N-representability. In this Letter we examine the algorithm and show its connection to the full configuration interaction method and the contracted Schroedinger equation. (C) 2002 Elsevier Science B.V. All rights reserved.