We report a new method for the purification of HiPCO single-wall carbon nanotubes (SWNT), which consists of the following sequence: (a) organic functionalization of the as-produced nanotubes (pristine tubes, p-SWNT), (b) purification of the soluble functionalized nanotubes (f-SWNT), (c) removal of the functional groups and recovery of purified nanotubes (r-SWNT) by thermal treatment at 350 degrees C, followed by annealing to 900 degrees C. Each of these steps contributes to the purification, but only their sequential combination leads to high-purity materials. Organic functionalization makes the SWNT more easy to handle, which results in a better manipulation for potential practical uses. The electronic properties of the purified tubes are investigated via Raman and NIR spectroscopies along with transmission electron microscopy.