A number of experimental works, mainly under extreme conditions, report a carbon phase with the same reflections as diamond but showing additional reflections that are forbidden for diamond. The crystal structure of this phase, called n-diamond by Hirai and Kondo (H. Hirai and K.-i. Kondo, Science 253 (1991) 772-774), remains unclear. By means of ab initio calculations based on density functional perturbation theory, the dynamical stability of the structures proposed to be n-diamond has been investigated up to a pressure of 30 GPa. According to the calculations, a tetragonal carbon allotrope, called glitter (M.J. Bucknum and R. Hoffman, J. Am. Chem. Soc. 116 (1994) 11456-11464), is the best candidate. The calculated electronic structure and bulk modulus of glitter are critically discussed.