  We perform a statistical analysis of the temporal and spectral properties of
the latest Fermi gamma-ray bursts (GRBs) to revisit the classification of GRBs.
We find that the bimodalities of duration and the energy ratio
($E_{\mathrm{peak}}$/Fluence) and the anti-correlation between spectral
hardness (hardness ratio ($HR$), peak energy and spectral index) and duration
($T_{90}$) support the long/soft $-$ short/hard classification scheme for Fermi
GRBs. The $HR - T_{90}$ anti-correlation strongly depends upon the spectral
shape of GRBs and energy bands, and the bursts with the curved spectra in the
typical BATSE energy bands show a tighter anti-correlation than those with the
power-law spectra in the typical BAT energy bands. This might explain why the
$HR - T_{90}$ correlation is not evident for those GRB samples detected by
instruments like {\it Swift} with a narrower/softer energy bandpass. We also
analyze the intrinsic energy correlation for the GRBs with measured redshifts
and well defined peak energies. The current sample suggests
$E_{\mathrm{p,rest}}=2455\times (E_{\mathrm{iso}}/10^{52})^{0.59}$ for short
GRBs, significantly different from that for long GRBs. However, both the long
and short GRBs comply with the same $E_{\mathrm{p,rest}}-L_{\mathrm{iso}}$
correlation.
