  A well-established method to deal with highly correlated systems is based on
the expansion of the Green's function in terms of spectral moments. In the
context of the Composite Operator Method one approximation is proposed: a set
of n composite fields is assumed as fundamental basis and the dynamics is
considered up to the order s. The resulting Green's function has a sn-pole
structure. The truncation of the hierarchy of the equations of motion is made
at the s-th order and the first s-1 equations are treated exactly. A theorem,
which rules the conservation of the spectral moments, is presented. The
procedure is applied to the Hubbard model and a recurrence relation for the
calculation of its electronic spectral moments is derived.
