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The band edge formalism of zero-average-index photonic band gap for the one-dimensional photonic crystals containing dispersion negative-index metamaterial is obtained. By adopting the band edge formalism, the upper and lower frequencies limits of the zero-average-index band gap are analyzed, and the results are in complete agreement with the results got by the projected band structure method. It is shown that the width and the band edge of the zero-average-index photonic band gap are significantly affected by the each constitutive parameter of the component materials of the one-dimensional photonic crystals. Based on the band edge formalism, new method of extending the zero-average-index photonic band gap has been presented by tuning the constitutive parameter of the component materials. Moreover, the conditions for zero width zero-average-index band gap are obtained. The realizability of tuning the constitutive parameter of the Drude dispersion metamaterial constructed by the nonresonant composite right/left-handed transmission structures is also discussed.