We have investigated by first principles the electronic, vibrational, and structural properties of bct C-4, a new form of crystalline sp(3) carbon recently found in molecular dynamics simulations of carbon nanotubes under pressure. This phase is transparent, dynamically stable at zero pressure, and more stable than graphite beyond 18.6 GPa. Coexistence of bct C-4 with M carbon can explain better the x-ray diffraction pattern of a transparent and hard phase of carbon produced by the cold compression of graphite. Its structure appears to be intermediate between that of graphite and hexagonal diamond. These facts suggest that bct C-4 is an accessible form of sp(3) carbon along the graphite-to-hexagonal diamond transformation path.