  We present a new measurement of the top quark mass in $t\bar t$ events in
which both $W$ bosons from top quarks decay into lepton ($e \nu,\mu \nu$).
  We use events collected by the CDF experiment from $p\bar p$ collisions at
\sqrt s=1.8 TeV at the Tevatron collider. We measure a top quark mass of 167.4
\pm 10.3(stat) \pm 4.8(syst) GeV/c^2 from a sample of eight events. We combine
this result with previous CDF measurements in other decay channels to obtain a
mass value of 176.0 \pm 6.5 GeV/c^2.
