Using first principles variable cell shape molecular dynamics, we predict a new structure for silica. This structure results from annealing α-quartz at pressures near a major phonon instability. The new phase is obtained by rotations of SiO4 tetrahedra producing edge-sharing SiO6 octahedra and SiO5 cuboids. This type of mechanism was proposed to account for structural transitions in silicate melts and amorphous solids under pressure. Here this mechanism is observed in a crystalline to crystalline phase transformation for the first time. The diffraction pattern of the new phase compares favorably with that of the unidentified intermediate crystalline phase found in silica during the amorphization.