Modulational instability (MI) of electomagnetic waves in an optical fiber near the zero dispersion point is investigated both analytical and numerical. The effect of fourth order dispersion is taken into account and a new region with MI is found. The possibility of MI is shown for the case of positive second and fourth order group dispersion. For both positive and negative fourth order dispersion a recurrence phenomenon is observed analogous to the Fermi-Paste-Ulam problem.