  The renormalizable extension of a pure Yang-Mills theory with Lorentz
violation is characterized by the CPT-Even $(k_F)_{\mu \nu \lambda \rho}$ and
the CPT-Odd $(k_{AF})_\mu$ constant Lorentz coefficients. In this paper, the
one-loop structure of the theory up to second order in these Lorentz violating
coefficients is studied using the BFM-gauge. Results for the diverse beta
functions are derived and contrasted with those given in the literature at
first order in these parameters. Special emphasis is putted on the beta
function $\beta(g)$, which is studied in both mass-independent and
mass-dependent renormalization schemes. It is found that in a mass-independent
scheme the $(k_{AF})_\mu$ Lorentz coefficient does not contribute to the
$\beta(g)$ function, but it does in a mass-dependent scheme with contributions
that are gauge-dependent and IR divergent.
