We measure time-dilation factors (TDFs) for 1158 long gamma-ray bursts (GRBs) using a peak-alignment method. Our standard corrections for noise bias and spectral redshift are implemented. Also for the first time we account for trigger bias against detecting relatively short, low signal-to-noise GRBs using a retriggering procedure which approximates the on-board BATSE algorithm on the 1024-ms timescale. This procedure implicitly addresses any bias that would be introduced when comparing bright bursts with dim bursts. The retriggering step significantly reduces the relative TDFs between the 10% brightest bursts and the 30% dimmest bursts. These corrected TDFs are compared with Monte Carlo simulations of a distribution of GRBs adopting standard cosmologies, GRB luminosity functions, and GRB rate-density evolution with cosmic time. Statistically, the corrected GRB TDFs are consistent with the expected extrinsic cosmological time dilation.

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