  It is well known that the family of Hahn polynomials
$\{h_n^{\alpha,\beta}(x;N)\}_{n\ge 0}$ is orthogonal with respect to a certain
weight function up to $N$. In this paper we present a factorization for Hahn
polynomials for a degree higher than $N$ and we prove that these polynomials
can be characterized by a $\Delta$-Sobolev orthogonality.
  We also present an analogous result for dual-Hahn, Krawtchouk, and Racah
polynomials and give the limit relations between them for all $n\in \XX N_0$.
Furthermore, in order to get this results for the Krawtchouk polynomials we
will get a more general property of orthogonality for Meixner polynomials.
