  In this letter we call into question the perturbatively parity breakdown at
1-loop for the massless QED_3 frequently claimed in the literature. As long as
perturbative quantum field theory is concerned, whether a parity anomaly owing
to radiative corrections exists or not will be definitely proved by using a
renormalization method independent of any regularization scheme. Such a problem
has been investigated in the framework of BPHZL renormalization method, by
adopting the Lowenstein-Zimmermann subtraction scheme. The 1-loop parity-odd
contribution to the vacuum-polarization tensor is explicitly computed in the
framework of the BPHZL renormalization method. It is shown that a Chern-Simons
term is generated at that order induced through the infrared subtractions --
which violate parity. We show then that, what is called parity anomaly, is in
fact a parity-odd counterterm needed for restauring parity.
