  The collection of a large number of $B$ hadron decays to hadronic final
states at the CDF II detector is possible due to the presence of a trigger that
selects events based on track impact parameters. However, the nature of the
selection requirements of the trigger introduces a large bias in the observed
proper decay time distribution. A lifetime measurement must correct for this
bias and the conventional approach has been to use a Monte Carlo simulation.
The leading sources of systematic uncertainty in the conventional approach are
due to differences between the data and the Monte Carlo simulation. In this
paper we present an analytic method for bias correction without using
simulation, thereby removing any uncertainty between data and simulation. This
method is presented in the form of a measurement of the lifetime of the $B^{-}$
using the mode B -> D0 pi. The $B^-$ lifetime is measured as $\tau_{B^-}$ =
1.663 $\pm$ 0.023 $\pm$ 0.015 ps, where the first uncertainty is statistical
and the second systematic. This new method results in a smaller systematic
uncertainty in comparison to methods that use simulation to correct for the
trigger bias.
