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 similar to 10(-8) K. A global six-dimensional H-2-H-2 potential-energy surface is adopted from a previous work [Boothroyd et al., J. Chem. Phys. 116, 666 (2002)]. State-resolved integral cross sections sigma(ij -> i'j')(epsilon(kin)) of different quantum-mechanical rotational transitions ij -> i'j' in the HD molecules and corresponding state-resolved thermal rate coefficients k(ij -> 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.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)