  We study the conformal invariance of non-planar beta-deformed N=4 SYM theory
using the coupling constant reduction (CCR) formalism. We show that up to order
g^10, differently from the planar case, we can remove the scheme dependence in
the definition of the theory without reducing to the real beta case. We also
compute the gauge beta function up to four loops and see that the generalized
finiteness theorems proposed in [hep-th: 0705.1483] still hold.
