  We calculate the next-to-next-to-leading order ${\cal O}(\alpha_s^4)$
one-loop squared corrections to the production of heavy quark pairs in
quark-antiquark annihilations. These are part of the next-to-next-to-leading
order ${\cal O}(\alpha_s^4)$ radiative QCD corrections to this process. Our
results, with the full mass dependence retained, are presented in a closed and
very compact form, in the dimensional regularization scheme. We have found very
intriguing factorization properties for the finite part of the amplitudes.
