  The dijet production cross section for jets containing a $b$-hadron
($b$-jets) has been measured in proton-proton collisions with a centre-of-mass
energy of $\sqrt{s} = 7$ TeV, using the ATLAS detector at the LHC. The data
used correspond to an integrated luminosity of 4.2 fb$^{-1}$. The cross section
is measured for events with two identified $b$-jets with a transverse momentum
$p_T > 20$ GeV and a minimum separation in the $\eta$-$\phi$ plane of $\Delta R
= 0.4$. At least one of the jets in the event is required to have $p_T > 270$
GeV. The cross section is measured differentially as a function of dijet
invariant mass, dijet transverse momentum, boost of the dijet system, and the
rapidity difference, azimuthal angle and angular distance between the $b$-jets.
The results are compared to different predictions of leading order and
next-to-leading order perturbative quantum chromodynamics matrix elements
supplemented with models for parton-showers and hadronization.
