  In our previous work, we searched for super-flares on different types of
stars while focusing on G-type dwarfs using entire Kepler data to study
statistical properties of the occurrence rate of super-flares. Using these new
data, as a by-product, we found fourteen cases of super-flare detection on
thirteen slowly rotating Sun-like stars with rotation periods of 24.5 to 44
days. This result supports earlier conclusion by others that the Sun may
possibly have a surprise super-flare. Moreover, we found twelve and seven new
cases of detection of exceptionally large amplitude super-flares on six and
four main-sequence stars of G- and M-type, respectively. No large-amplitude
flares were detected in A, F, or K main-sequence stars. Here we present
preliminary analysis of these cases. The super-flare detection, i.e. an
estimation of flare energy, is based on a more accurate method compared to
previous studies. We fit an exponential decay function to flare light curves
and study the relation between e-folding decay time, $\tau$, vs. flare
amplitude and flare energy. We find that for slowly rotating Sun-like stars,
large values of $\tau$ correspond to small flare energies and small values of
$\tau$ correspond to high flare energies considered. Similarly, $\tau$ is large
for small flare amplitudes and $\tau$ is small for large amplitudes considered.
However, there is no clear relation between these parameters for large
amplitude super-flares in the main sequence G- and M-type stars, as we could
not establish clear functional dependence between the parameters via standard
fitting algorithms.
