Abstract: In a column provided with internals for liquid/gas contacting, the sour water feedstock is stripped using steam, then cooled by a cold liquid and washed using cold water injection. This method allows to separate an ammonia-poor (5-5000 ppm) H2S gaseous effluent and an H2S-lean (100-1000 ppm for example) purified water. The method is yet improved by adding a second column that receives the purified water from the first column and separates the hydrogen sulfide and the ammonia according to the method operated in the first column. The purified water from the second column is preferably partially injected into the first and/or the second column as wash water. A facility for implementing the method according to the invention.