We analyze the modulation instability spectrum in a varying dispersion optical fiber as a function of the dispersion oscillation amplitude. For large dispersion oscillations, we predict a novel sideband splitting into different sub-sidebands. The emergence of the new sidebands is observed whenever the classical perturbation analysis for parametric resonances predicts vanishing sideband amplitudes. The numerical results are in good quantitative agreement with Floquet or Bloch stability analysis of four-wave mixing in the periodic dispersion fiber. We have also shown that linear gain or loss may have a dramatic influence in reshaping the new sidebands.