The second-order Raman spectra of diamond and silicon have been calculated using ab initio phonons and phenomenological polarizability coefficients. The sharp peak in the spectrum of diamond near the two-phonon cutoff is explained by a maximum in the vibrational density of states; this maximum originates from the uppermost phonon branch whose frequencies are calculated to have a minimum at the Brillouin-zone center. This frequency minimum as well as the sharp Raman peak are unique to diamond and do not occur for the other group-IV semiconductors. In our calculation based on harmonic ab initio lattice dynamics neither two-phonon bound states nor polarizability matrix element effects are needed to explain the peak, and we feel that the long-standing controversy about its origin has been resolved.