We report the results of an improved determination of the triple correlation DP·(p(e)×p(v)) that can be used to limit possible time-reversal invariance in the beta decay of polarized neutrons and constrain extensions to the standard model. Our result is D=[-0.96±1.89(stat)±1.01(sys)]×10(-4). The corresponding phase between gA and gV is ϕAV=180.013°±0.028° (68% confidence level). This result represents the most sensitive measurement of D in nuclear β decay.