The quantum‐mechanical method of distorted waves for calculating the rotational relaxation rates in H2as developed by Brout is used here to calculate the relaxation time for the &Dgr;J=±2 rotational transitions of linear polyatomic CO2by taking into account the higher partial wave contributions. The intermolecular potential used consists of a spherical part and a nonspherical part with a constant parameter to characterize the deviation of the potential from spherical symmetry. The results obtained indicate that the collision numberZ(and hence the relaxation time &tgr;) is a monotonically decreasing function of the temperatureTfor a givenJand is a monotonically increasing function ofJfor a givenT. Except for small values ofJ, Zand &tgr; for a givenTare both approximately proportional to exp(aJ), whereais a constant. Detailed numerical results are also obtained and compared with known experimental results. It is shown that the method used here is not valid when the temperature is too high or wheneverZbecomes too close to 1.