The thermal transport properties of single-wall carbon nanotubes (SWCNTs) are re-investigated using the iterative solution of the Boltzmann transport equation by including four-phonon scattering. Using only three-phonon scattering, the flexural and twisted phonon modes are found to remain non-scattered via Umklapp processes, resulting in the literature-reported divergence of thermal conductivity with tube length. However, with four-phonon scattering, while longitudinal modes remain unaffected, the otherwise non-scattered transverse modes undergo Umklapp scattering and result in a non-ballistic transport, thus settling a decades-long debate on the length dependence of thermal conductivity of SWCNTs. The predicted thermal conductivity of SWCNTs using both three- and four-phonon scatterings is 3700 W/m-K at 300 K and stays highest amongst all known materials.