  Almost all known instanton solutions in noncommutative Yang-Mills theory have
been obtained in the modified ADHM scheme. In this paper we employ two
alternative methods for the construction of the self-dual U(2) BPST instanton
on a noncommutative Euclidean four-dimensional space with self-dual
noncommutativity tensor. Firstly, we use the method of dressing
transformations, an iterative procedure for generating solutions from a given
seed solution, and thereby generalize Belavin's and Zakharov's work to the
noncommutative setup. Secondly, we relate the dressing approach with Ward's
splitting method based on the twistor construction and rederive the solution in
this context. It seems feasible to produce nonsingular noncommutative
multi-instantons with these techniques.
