  The $\gamma_i$-deformed $\mathcal{N}=4$ super-Yang-Mills theory is a
non-supersymmetric deformation of the maximally-supersymmetric gauge theory in
four dimensions which is conformally-invariant at the planar level. At the
non-planar level non-trivial renormalization of marginal double-trace operators
appears to break conformal invariance. At non-planar level, however, the
behavior of this theory is less well understood. We study the one loop
renormalization of the theory and the resulting flow of Yukawa and scalar
coupling at the order ${\cal O}(\frac{\lambda}{N^2})$, and find $\gamma_i$
parameters receive nontrivial quantum corrections. We show that, at low
energies, the $\gamma_i$ parameters flow to a common value and
$\gamma_i$-deformed theory reaches an $\mathcal{N}=1$-supersymmetric fixed
point described by the $\beta$-deformed $\mathcal{N}=4$ super Yang-Mills
theory.
