Hydrogen peroxide in high yields can be generated with high efficiency at mild conditions (25 degrees C and atmospheric pressure) with the formation of only environment-friendly by-products (N2 and H2O) by a reduction of O2 by hydrazine from its hydrate/salt with its complete conversion in a short reaction period (<or=0.5 h) using a easily separable supported Pd catalyst (Pd/Al2O3, Pd/Ga2O3 or Pd/C) in an acidic aqueous medium in the presence of bromide anions; the presence of both acid (protons) and bromide anions is essential for the selective reduction of O2 by hydrazine to H2O2 and in their absence, the reaction leads only to the formation of water.