  In this article, we establish the adjoint equation for
Nikiforov-Uvarov-Suslov difference equation of hypergeometric type on
non-uniform lattices, and prove it to be a difference equation of
hypergeometric type on non-uniform lattices as well. The particular solutions
of the adjoint equation are then obtained. As an appliction of these particular
solutions, we use them to obtain the particular solutions for the original
difference equation of hypergeometric type on non-uniform lattices. Finally, we
prove another kind of fundamental theorems for Nikiforov-Uvarov-Suslov
difference equation of hypergeometric type, which are essentially new results,
its expression is different from Suslov's Theorem.
