This Letter presents an investigation into the temperature dependence of the relaxation cross-section of the mean rotational energy, sigma(rot), in carbon monoxide. Our data obtained in a free jet at 20-200 K together with high-temperature measurements made by other authors point to non-monotonic behavior of the rotational relaxation cross-section as a function of temperature. A theoretical explanation for such a behavior of sigma(rot) with temperature is offered. (C) 1999 Elsevier Science B.V. All rights reserved.