Abstract Rate coefficients for pure rotational quenching in H2(ν 1 = 0, j 1) + H2(ν 2 = 0, j 2) collisions from initial levels of j 1 = 2–31 (j 2 = 0 or 1) to all lower rotational levels are presented. We carried out extensive quantum mechanical close-coupling calculations based on a recently published H2–H2 potential energy surface (PES) developed by Patkowski et al. that has been demonstrated to be more reliable than previous work. Rotational transition cross sections with initial levels of j 1 = 2–14, 18, 19, 24, and 25 were computed for energies ranging from 10−6 to 1000 cm−1, while the coupled-states approximation was adopted from 2000 to 20,000 cm−1. The corresponding rate coefficients were calculated for the temperature range 10−5 ≤ T ≤ 10,000 K. Scaling methods based on the ultra-cold data (10−5–1 K) were used to estimate rate coefficients for all other intermediate rotational states. Comparisons with previous work that adopted different PESs show small discrepancies at high temperatures and in low-energy resonance regions. The astrophysical applications of the current results are briefly discussed, including the rotational H2 critical densities due to para-H2 and ortho-H2 collisions.