  We present a new method to search for candidate z~>2 Herschel 500{\mu}m
sources in the GOODS-North field, using a S500{\mu}m/S24{\mu}m "color
deconfusion" technique. Potential high-z sources are selected against
low-redshift ones from their large 500{\mu}m to 24{\mu}m flux density ratios.
By effectively reducing the contribution from low-redshift populations to the
observed 500{\mu}m emission, we are able to identify counterparts to high-z
500{\mu}m sources whose 24{\mu}m fluxes are relatively faint. The recovery of
known z~4 starbursts confirms the efficiency of this approach in selecting
high-z Herschel sources. The resulting sample consists of 34 dusty star-forming
galaxies at z~>2. The inferred infrared luminosities are in the range
1.5x10^12-1.8x10^13 Lsun, corresponding to dust-obscured star formation rates
(SFRs) of ~260-3100 Msun/yr for a Salpeter IMF. Comparison with previous SCUBA
850{\mu}m-selected galaxy samples shows that our method is more efficient at
selecting high-z dusty galaxies with a median redshift of z=3.07+/-0.83 and 10
of the sources at z~>4. We find that at a fixed luminosity, the dust
temperature is ~5K cooler than that expected from the Td-LIR relation at z<1,
though different temperature selection effects should be taken into account.
The radio-detected subsample (excluding three strong AGN) follows the
far-infrared/radio correlation at lower redshifts, and no evolution with
redshift is observed out to z~5, suggesting that the far-infrared emission is
star formation dominated. The contribution of the high-z Herschel 500{\mu}m
sources to the cosmic SFR density is comparable to that of SMG populations at
z~2.5 and at least 40% of the extinction-corrected UV samples at z~4
(abridged).
