A matrix parameterization of the 15 μm CO2 band radiative cooling in the middle and upper terrestrial atmosphere for both local thermodynamic equilibrium (LTE) and non-LTE (NLTE) layers is proposed. For the atmospheric region between ~13 and 85 km, matrix coefficients for CO2 concentrations of 150, 360, 540, and 720 ppm have been precalculated using a line-by-line technique. A method for interpolation of the matrix coefficients for arbitrary CO2 concentration is suggested. In the layer between 85 and 110 km, where strong NLTE effects start to occur, a recurrence formula relating cooling rate values at two neighboring altitude levels is used. To calculate the cooling rate above 110 km, a simple approach accounting for both the absorption of the radiative flux formed below 110 km and the cooling-to-space terms is suggested. The accuracy of the parameterization is examined for different temperature and CO2 profiles as well as for different atomic oxygen concentrations in the NLTE layer. ¿ 1998 American Geophysical Union