We show that the recently proposed formulation of non-commutative N = 2 Sup
er Yang-Mills theory implies that the commutative and non-commutative effec
tive coupling constants tau (u) and tau (nc)(u) coincide. We then introduce
a key relation which allows to find a non-trivial solution of such equatio
n, thus fixing the form of the low-energy effective action. The dependence
on the non-commutative parameter arises from a rational function deforming
the Seiberg-Witten differential.