  For top quark decays into heavy quark mesons $\Upsilon$ and $\bar{B}_c^*$ , a
complete calculation to the leading order both in QCD coupling constant
$\alpha_s$ and in $v$, the typical velocity of the heavy quarks inside the
mesons, is performed. Relatons between the top quark mass and the decay
branching ratios are studied. Comparion with the results which are obtained by
using the quark frangmentation functions is also discussed. The branching
ratios are consistent (within a factor of $2\sim 3 $) with that obtained using
fragmentation functions at $m_t\sim 150$ GeV.
