  A non homogeneous spin chain in the representations $ \{3 \}$ and $ \{3^*\}$
of $A_2$ is analyzed. We find that the naive nested Bethe ansatz is not
applicable to this case. A method inspired in the nested Bethe ansatz, that can
be applied to more general cases, is developed for that chain. The solution for
the eigenvalues of the trace of the monodromy matrix is given as two coupled
Bethe equations different from that for a homogeneous chain. A conjecture about
the form of the solutions for more general chains is presented.
  PACS: 75.10.Jm, 05.50+q 02.20 Sv
