  We employ the twistor approach to the construction of U(2) multi-instantons
`a la 't Hooft on noncommutative R^4. The noncommutative deformation of the
Corrigan-Fairlie-'t Hooft-Wilczek ansatz is derived. However, naively
substituting into it the 't Hooft-type solution is unsatisfactory because the
resulting gauge field fails to be self-dual on a finite-dimensional subspace of
the Fock space. We repair this deficiency by a suitable Murray-von Neumann
transformation after a specific projection of the gauge potential. The proper
noncommutative 't Hooft multi-instanton field strength is given explicitly, in
a singular as well as in a regular gauge.
