  In this study we show that the sum of the powers of arbitrary products of
quantum spin operators such as $(S^+)^l(S^-)^m(S^z)^n$ can be reduced by one
unit, if this sum is equal to 2S+1, S being the spin quantum number. We
emphasize that by a repeated application of this procedure \em all \em
arbitrary spin operator products with a sum of powers larger than 2S can be
replaced by a combination of spin operators with a maximum sum of powers not
larger than 2S. This transformation is exact. All spin operators must belong to
the same lattice site. By use of this procedure the consideration of single-ion
anisotropies and the investigation of the magnetic reorientation within a
Green's function theory are facilitated. Furthermore, it may be useful for the
study of time dependent magnetic properties within the ultrashort (fsec) time
domain.
