  The QCD sum rule calculation of the in-medium pion decay constants using
pseudoscalar-axial vector correlation function, $i \int d^4x e^{ip\cdot x} <
\rho| T[{\bar d}(x) i \gamma_5 u (x) {\bar u}(0) \gamma_\mu \gamma_5 d (0)] |
\rho>$ is revisited. In particular, we argue that the dimension 5 condensate,
$<{\bar q} (i D_0)^2 q >_N + {1\over 8} < {\bar q} g_s \sigma \cdot {\cal G} q
>_N$, which is crucial for splitting the time ($f_t$) and space ($f_s$)
components of the decay constant, is not necessarily restricted to be positive.
Its positive value is found to yield a tachyonic pion mass. Using the in-medium
pion mass as an input, we fix the dimension 5 condensate to be around $-0.025
{\rm GeV}^2 \sim -0.019$ GeV$^2$. The role of the $N$ and $\Delta$ intermediate
states in the correlation function is also investigated. The $N$ intermediate
state is found not to contribute to the sum rules. For the $\Delta$
intermediate state, we either treat it as a part of the continuum or propose a
way to subtract explicitly from the sum rules. With (and without) explicit
$\Delta$ subtraction while allowing the in-medium pion mass to vary within 139
MeV $ \le m_\pi^* \le$ 159 MeV, we obtain $f_s/f_\pi = 0.37 \sim 0.78$ and $f_t
/ f_\pi = 0.63 \sim 0.79$.
