The vibrational properties of amorphous SiO2 were studied within first-principles density functional theory. The calculated spectrum is in good agreement with neutron data, showing, in particular, a double peak in the high-frequency region. This doublet results from different local modes of the tetrahedral subunits and cannot be ascribed to a longitudinal-optic-transverse-optic (LO-TO) effect. This solves a long-standing controversy about the origin of the doublet in neutron spectra. A LO-TO splitting is recovered only when the long-wavelength limit is probed, as in optical experiments. These findings should be a general feature of tetrahedral AX(2) amorphous networks.