  Contractor renormalization group (CORE) method is applied to the SU($N$)
chain and ladders in this paper. In our designed schemes, we show that these
two classes of systems can return to their original form of Hamiltonian after
CORE transformation. Successive iteration of the transformation leads to a
fixed point so that the ground state energy and the energy gap to the ground
state can be deduced. The result of SU($N$) chain is compared with the one by
Bethe ansatz method. The transformation on spin-1/2 ladders gives a finite gap
in the excited energy spectra to the ground state in an intuitive way. The
application to SU(3) ladders is also discussed.
