A process for the removal of hydrogen sulfide and sulfur recovery from a H2S-containing gas stream by catalytic direct oxidation and Claus reaction through two or more serially connected catalytic reactors, wherein a specific control of the oxygen supplement is operated. The control and improvement of the process is obtained by complementing, in each major step of the process, the H2S-containing gas stream by a suitable flow of oxygen, namely before the H2S-containing gas stream enters the Claus furnace, in the first reactor of the process and in the last reactor of the process. Especially in application in a SubDewPoint sulfur recovery process the H2S/SO2 ratio is kept constant also during switch-over of the reactors R1 and R by adding the last auxiliary oxygen containing gas directly upstream the last reactor R so that the H2S/SO2 ratio can follow the signal of the ADA within a few seconds.