  Projections play crucial roles in the ADHM construction on noncommutative
$\R^4$. In this article a framework for the description of equivalence
relations between projections is proposed. We treat the equivalence of
projections as ``gauge equivalence'' on noncommutative space. We find an
interesting application of this framework to the study of U(2) instanton on
noncommutative $\R^4$: A zero winding number configuration with a hole at the
origin is ``gauge equivalent'' to the noncommutative analog of the BPST
instanton. Thus the ``gauge transformation'' in this case can be understood as
a noncommutative resolution of the singular gauge transformation in ordinary
$\R^4$.
