  We investigate some issues on renormalisability of non-anticommutative
supersymmetric gauge theory related to field redefinitions. We study one loop
corrections to $N=\frac{1}{2}$ supersymmetric $SU(N)\times U(1)$ gauge theory
coupled to chiral matter in component formalism, and show the procedure which
has been introduced for renormalisation is problematic because some terms which
are needed for the renormalisability of theory are missed from the Lagrangian.
In order to prove the theory is renormalisable, we redefine the gaugino and the
auxiliary fields($\lambda, \bar F$), which result in a modified form of the
Lagrangian in the component formalism. Then, we show the modified Lagrangian
has extra terms which are necessary for renormalisability of
non-anticommutative supersymmetric gauge field theories. Finally we prove $N =
\frac{1}{2}$ supersymmetric gauge theory is renormalisable up to one loop
corrections using standard method of renormalisation; besides, it is shown the
effective action is gauge invariant.
