The standard model of particle physics contains parameters—such as particle masses—whose origins are still unknown and which cannot be predicted, but whose values are constrained through their interactions. In particular, the masses of the top quark (Mt) and W boson (MW)1 constrain the mass of the long-hypothesized, but thus far not observed, Higgs boson. A precise measurement of Mt can therefore indicate where to look for the Higgs, and indeed whether the hypothesis of a standard model Higgs is consistent with experimental data. As top quarks are produced in pairs and decay in only about 10-24 s into various final states, reconstructing their masses from their decay products is very challenging. Here we report a technique that extracts more information from each top-quark event and yields a greatly improved precision (of 5.3 GeV/c2) when compared to previous measurements2. When our new result is combined with our published measurement in a complementary decay mode3 and with the only other measurements available2, the new world average for Mt becomes4 178.0 4.3 GeV/c2. As a result, the most likely Higgs mass increases from the experimentally excluded5 value6 of 96 to 117 GeV/c2, which is beyond current experimental sensitivity. The upper limit on the Higgs mass at the 95% confidence level is raised from 219 to 251 GeV/c2.