Recent Swift observations suggest that the traditional long vs. short GRB classification scheme does not always associate GRBs to the two physically motivated model types, i.e. Type II (massive star origin) vs. Type I (compact star origin). We propose a new phenomenological classification method of GRBs by introducing a new parameter epsilon=E_gamma, iso,52/E^5/3_p,z,2, where E_γ,iso is the isotropic gamma-ray energy (in units of 10^52 erg), and E_p,z is the cosmic rest frame spectral peak

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... y (in units of 100 keV). For those short GRBs with "extended emission", both quantities are defined for the short/hard spike only. With the current complete sample of GRBs with redshift and E_p measurements, the epsilon parameter shows a clear bimodal distribution with a separation at epsilon 0.03. The high-epsilon region encloses the typical long GRBs with high-luminosity, some high-z "rest-frame-short" GRBs (such as GRB 090423 and GRB 080913), as well as some high-z short GRBs (such as GRB 090426). All these GRBs have been claimed to be of the Type II origin based on other observational properties in the literature. All the GRBs that are argued to be of the Type I origin are found to be clustered in the low-epsilon region. They can be separated from some nearby low-luminosity long GRBs (in 3sigma) by an additional T_90 criterion, i.e. T_90,z< 5 s in the Swift/BAT band. We suggest that this new classification scheme can better match the physically-motivated Type II/I classification scheme.