  The in-medium pion properties, {\it i.e.} the temporal pion decay constant
$f_t$, the pion mass $m_\pi^*$ and the wave function renormalization, in
symmetric nuclear matter are calculated in an in-medium chiral perturbation
theory up to the next-to-leading order of the density expansion $O(k_F^4)$. The
chiral Lagrangian for the pion-nucleon interaction is determined in vacuum, and
the low energy constants are fixed by the experimental observables. We
carefully define the in-medium state of the pion and find that the pion wave
function plays an essential role for the in-medium pion properties. We show
that the linear density correction is dominated and the next-leading
corrections is not so large at the saturation density, while their
contributions can be significant in higher densities. The main contribution of
the next-leading order comes from the double scattering term. We also discuss
whether the low energy theorems, the Gell-Mann--Oakes--Renner relation and the
Glashow--Weinberg relation, are satisfied in nuclear medium beyond the linear
density approximation. We find also that the wave function renormalization is
enhanced as largely as $50\%$ at the saturation density including the
next-leading contribution and the wave function renormalization could be
measured in the in-medium $\pi^0\to \gamma\gamma$ decay.
