Infrared emission from (CO)-C-12 and (CO)-C-13, excited in the cathode region of a discharge tube immersed in liquid nitrogen, was recorded by Fourier-transform spectrometry at a resolution of 0.005 cm(-1). The Delta v=1 sequence bands recorded in the 2500-1800 cm(-1) spectral interval, indicate the existence of three different rotational populations; (i) molecules in the zero-ground level with T(rot)approximate to 100 K (responsible for reabsorption of part of the 1-0 emission band); (ii) molecules with T(rot)approximate to 275 K (maximum intensity for J(max)'approximate to 6 in each band, T(vib)approximate to 3000 K for v'=2-4, T(vib)approximate to 8600 K for v'=5-13); (iii) molecules with v' limited to 6, for which R-rotational lines are observed for J' values between 50 and 120 (J(max)'approximate to 90, non-Boltzmannian population distribution). The full-width at half-maximum (FWHM) of all the observed lines is less than 0.007 cm(-1). A Doppler width of 0.005 cm(-1) and translational temperature T(tr)approximate to 280 K can be deduced. Such high-J levels of the CO molecule had never been observed in the laboratory. In the absorption spectrum of the Sun photosphere, the same lines present FWHM values 5-8 times larger. The best available Dunham coefficients are checked to reproduce the high-J lines wave numbers to at least 0.001 cm(-1). Dissociative recombination of the dimer (CO)(2)(+) cation, which is likely to be formed in our experimental conditions, is discussed as a possible mechanism to produce CO fragments with very high rotational excitation, while keeping vibrational excitation limited to v'=6.