We report a novel phenomenon for carbon nanotube growth that results in a new carbon nanotube morphology. A carbon nanotube grown via metal nanoparticle-catalyzed chemical vapor deposition splits into two flattened nanotubes during growth and the two flattened nanotubes merge to form a ring of carbon nanotube/nanoribbon. This novel process is revealed by transmission electron microscopy observations of the carbon nanostructures. We propose that the splitting-and-joining process involves only one metal catalyst nanoparticle and a self-folding mechanism that we have named the origami mechanism to explain the process and the formation of nanoribbons and nanotetrahedra.