  The background gauge renormalization of the first order formulation of the
Yang-Mills theory is studied by using the BRST identities. Together with the
background symmetry, these identities allow for an iterative proof of
renormalizability to all orders in perturbation theory. However, due to the
fact that certain improper diagrams which violate the BRST symmetry should be
removed, the renormalizability must be deduced indirectly. The recursive method
involves rescalings and mixings of the fields, which lead to a renormalized
effective action for the background field theory.
