  Report is made of a systematic scaling study of the finite-temperature chiral
phase transition of two-flavor QCD with the Kogut-Susskind quark action based
on simulations on $L^3\times4$ ($L$=8, 12 and 16) lattices at the quark mass of
$m_q=0.075, 0.0375, 0.02$ and 0.01. Our finite-size data show that a phase
transition is absent for $m_q\geq 0.02$, and quite likely also at $m_q=0.01$.
The scaling behavior of susceptibilities as a function of $m_q$ is consistent
with a second-order transition at $m_q=0$. However, the exponents deviate from
the O(2) or O(4) values theoretically expected.
