  This supplementary manuscript is to describe an important nontrivial example,
which appears in the matrix model of type IIB in the super string theory in
order to apply a new duality for the moduli spaces of Yang-Mills connections on
noncommutative vector bundles. Actually, the moduli space of the instanton
bundle over noncommutative Euclidean 4-spaces with respect to the canonical
action of space translations is computed precisely without using the ADHM-
construction.
