  We introduce the -1 dual Hahn polynomials through an appropriate $q \to -1$
limit of the dual q-Hahn polynomials. These polynomials are orthogonal on a
finite set of discrete points on the real axis, but in contrast to the
classical orthogonal polynomials of the Askey scheme, the -1 dual Hahn
polynomials do not exhibit the Leonard duality property. Instead, these
polynomials satisfy a 4-th order difference eigenvalue equation and thus
possess a bispectrality property. The corresponding generalized Leonard pair
consists of two matrices $A,B$ each of size $N+1 \times N+1$. In the eigenbasis
where the matrix $A$ is diagonal, the matrix $B$ is 3-diagonal; but in the
eigenbasis where the matrix $B$ is diagonal, the matrix $A$ is 5-diagonal.
