  A close coupling quantum-mechanical calculation is performed for rotational
energy transfer in a HD+HD collision at very low energy, down to the ultracold
temperatures: $T \sim 10^{-8}$ K. A global six-dimensional H$_2$-H$_2$
potential energy surface is adopted from a previous work [Boothroyd {\it et
al.}, J. Chem. Phys., {\bf 116}, 666 (2002).] State-resolved integral cross
sections $\sigma_{ij\rightarrow i'j'}(\varepsilon_{kin})$ of different
quantum-mechanical rotational transitions $ij\rightarrow i'j'$ in the HD
molecules and corresponding state-resolved thermal rate coefficients
$k_{ij\rightarrow i'j'}(T)$ have been computed. Additionally, for comparison,
H$_2$+H$_2$ calculations for a few selected rotational transitions have also
been performed. The hydrogen and deuterated hydrogen molecules are treated as
rigid rotors in this work. A pronounced isotope effect is identified in the
cross sections of these collisions at low and ultracold temperatures.
