  We show the relation of the non-stationary difference equation proposed by
one of the authors and the quantized discrete Painlev\'e VI equation. The
five-dimensional Seiberg-Witten curve associated with the difference equation
has a consistent four-dimensional limit. We also show that the original
equation can be factorized as a coupled system for a pair of functions
$\bigl(\mathcal{F}^{(1)},\mathcal{F}^{(2)}\bigr)$, which is a consequence of
the identification of the Hamiltonian as a translation element in the extended
affine Weyl group. We conjecture that the instanton partition function coming
from the affine Laumon space provides a solution to the coupled system.
