We have studied the high energy optical transitions of semiconducting single-walled carbonnanotubes using the nonorthogonal tight-binding model, which takes into account the excitoneffect. It is found from our calculations that the exciton’s binding energies for the high energyE33 and E44 transitions are large enough, indicating clearly they are also excitonic in nature. Moreimportantly, the logarithmic Kane–Mele correction, successful for the low energyE11 and E22 transitions, is now found to fail for describing the many-body effects in the higher energytransitions, which is consistent with the experimental result of Araujo et al (2007 Phys. Rev.Lett. 98 067401). Finally, it is interesting to find the possibility of a crossover effect between theE33 and E44 energies for certain mod 1 chiralities and the family behavior of the many-body corrections in theE33 and E44 transitions, both of which are well supported by the recent experiment of Haroz et al (2008Phys. Rev. B 77 125405).