The BL Lac object H1426+428 was recently detected as a high-energy γ-ray source by the VERITAS collaboration (Horan et al.). We have reanalyzed the 2001 portion of the data used in the detection in order to examine the spectrum of H1426+428 above 250 GeV. We find that the time-averaged spectrum agrees with a power law of the shape The statistical evidence from our data for emission above 2.5 TeV is 2.6 σ. At the 95% confidence level, the integral flux of H1426+428 above 2.5 TeV is larger than 3% of the corresponding flux from the Crab Nebula. The spectrum is consistent with the (noncontemporaneous) measurement by Aharonian et al. both in shape and in normalization. Below 800 GeV, the data clearly favor a spectrum steeper than that of any other TeV blazar observed so far, indicating a difference in the processes involved either at the source or in the intervening space.