Flattening of a carbon nanotube results in the formation of a carbon nanoribbon with well-defined edges. In addition, a switching of the flattening direction by about a right angle yields a carbon nanotetrahedron at the switching point in a nanoribbon. Here, we report that chains of carbon nanotetrahedra/nanoribbons are formed via sequential switching of the flattening direction of multiwalled carbon nanotubes, in which neighboring two nanotetrahedra are connected by a short nanoribbon, namely a flattened nanotube. We suggest that the formation of nanotetrahedra chains is caused by a quasi-periodic instability of catalyst iron nanoparticles during the chemical vapor deposition growth. In addition, two adjoining carbon nanotetrahedra were found.