  By using the drone-fermion representation and the Schwinger-Keldysh approach,
we calculate the current noise and the charge noise for a single-electron
transistor in the non-equilibrium state in the presence of large quantum
fluctuation of island charge. Our result interpolates between those of the
"orthodox theory" and the "co-tunneling theory". We find the following effects
which are not treated by previous theories: (i) At zero temperature T=0 and at
finite applied bias voltage $|eV| \gg T_{K}$, where $T_{K}$ is the "Kondo
temperature", we find the Fano factor is suppressed more than the suppression
caused by Coulomb correlation both in the Coulomb blockade regime and in the
sequential tunneling regime. (ii) For $T \gg |eV|/2 \gg T_{K}$, the current
noise in the presence of large charge fluctuation is modified and deviates from
the prediction of the orthodox theory. However, the Fano factor coincides with
that of the orthodox theory and is proportional to the temperature. (iii) For
$eV, T \lesssim T_{K}$, the charge noise is suppressed due to the
renormalization of system parameters caused by quantum fluctuation of charge.
We interpret it in terms of the modification of the "unit" of the island
charge.
