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).
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