  We report a measurement of the top quark mass, M_t, in the dilepton decay
channel of $t\bar{t}\to b\ell'^{+}\nu_{\ell'}\bar{b}\ell^{-}\bar{\nu}_{\ell}$
using an integrated luminosity of 1.0 fb^{-1} of p\bar{p} collisions collected
with the CDF II detector. We apply a method that convolutes a leading-order
matrix element with detector resolution functions to form event-by-event
likelihoods; we have enhanced the leading-order description to describe the
effects of initial-state radiation. The joint likelihood is the product of the
likelihoods from 78 candidate events in this sample, which yields a measurement
of M_{t} = 164.5 \pm 3.9(\textrm{stat.}) \pm 3.9(\textrm{syst.})
\mathrm{GeV}/c^2, the most precise measurement of M_t in the dilepton channel.
