The cooling rate due to the 9.6μm band of ozone has been calculated by a new approxi-mation. Comparison with the results of the exact line-by-line integration shows that usingthis now approach makes it possible to accurately deal with integrations over wavenumber andover zenith angle and inhomogeneities of the atmosphere which have been left unsolved satis-factorily. This procedure is remarkably fast. It is also shown that the Curtis-Godson ap-proximation and the diffuse factor of 1.667 used in the usual band model techniques areinadequate for the 9.6μm ozone band. The cooling rate due to the 9.6μm band of ozone has been calculated by a new approxi-mation. Comparison with the results of the exact line-by-line integration shows that usingthis now now makes it possible to accurately deal with integrations over wavenumber andover zenith angle and inhomogeneities of the atmosphere which have been left unsolved satis-factorily. This procedure is remarkably fast. It is also shown in the Curtis-Godson ap-proximation and the diffuse factor of 1.667 used in the usual band model techniques are indedectible for the 9.6μm ozone band.