  We develop the noncommutative harmonic space (NHS) analysis to study the
problem of solving the non-linear constraint eqs of noncommutative Yang-Mills
self-duality in four-dimensions. We show that this space, denoted also as
NHS($\eta,\theta$), has two SU(2) isovector deformations $\eta^{(ij)}$ and
$\theta^{(ij)}$ parametrising respectively two noncommutative harmonic
subspaces NHS($\eta,0$) and NHS($0,\theta$) used to study the self-dual and
anti self-dual noncommutative Yang-Mills solutions. We formulate the Yang-Mills
self-dual constraint eqs on NHS($\eta,0$) by extending the idea of harmonic
analyticity to linearize them. Then we give a perturbative self-dual solution
recovering the ordinary one. Finally we present the explicit computation of an
exact self-dual solution.
