Modulational instability (MI) of electromagnetic waves in a birefringent fiber with a periodic dispersion (two-step dispersion management scheme) is investigated. The properties of new sidebands are studied. The strong variation of dispersion leads to the decreasing of the main MI region and the suppression of additional resonance. In the random dispersion case the MI of all frequencies of modulation in the normal dispersion region is predicted. In the anomalous dispersion case the decreasing of the main MI peak is calculated and changes in the spectral bandwidth of MI gain are found. The analytical predictions are confirmed by the numerical simulations of the full coupled nonlinear Schrödinger equations with periodic coefficients.