  We study one loop corrections to $N=\frac{1}{2}$ supersymmetric $SU(N)\times
U(1)$ pure gauge theory. We calculate divergent contributions of the 1PI graphs
contain the non-anti-commutative parameter $C$ up to one loop corrections. We
find the disagreement between component formalism and superspace formalism is
because of the field redefinition in component case. We modify gaugino field
redefinition and lagrangian. We show extra terms of lagrangian have been
generated by $\lambda$ redefinition and are necessary for the renormalisation
of the theory. Finally we prove $N = \frac{1}{2}$ supersymmetric gauge theory
is renormalisable up one loop corrections using standard method of
renormalisation
