  Gamma-ray bursts (GRBs) are believed to belong to two classes and they are
conventionally divided according to their durations. This classification scheme
is not satisfied due to the fact that duration distributions of the two classes
are heavily overlapped. We collect a new sample (153 sources) of GRBs and
investigate the distribution of the logarithmic deviation of the $E_p$ value
from the Amati relation. The distribution possesses an obvious bimodality
structure and it can be accounted for by the combination of two Gaussian
curves. Based on this analysis, we propose to statistically classify GRBs in
the well-known $E_{p}$ vs. $E_{iso}$ plane with the logarithmic deviation of
the $E_p$ value. This classification scheme divides GRBs into two groups: Amati
type bursts and non-Amati type bursts. While Amati type bursts well follow the
Amati relation, non-Amati type bursts do not. It shows that most Amati type
bursts are long duration bursts and the majority of non-Amati type bursts are
short duration bursts. In addition, it reveals that Amati type bursts are
generally more energetic than non-Amati type bursts. An advantage of the new
classification is that the two kinds of burst are well distinguishable and
therefore their members can be identified in certainty.
