A method for improving drastically both the selectivity and yield of hydrogen peroxide in the direct oxidation of hydrogen to hydrogen peroxide over a solid catalyst comprising palladium, which comprises: i) depositing on the solid catalyst at least two halogen containing compounds, one compound essentially comprising bromine and second compound essentially comprising fluorine with the bromine to palladium and fluorine to palladium atom ratios in the range from 0.02 to 20 and from 0.01 to 50, respectively; ii) decomposing the halo compounds deposited on the solid catalyst by calcination at a temperature above 200.degree. C. under inert, reducing or oxidizing gas atmosphere or under vacuum; and iii) contacting the solid catalyst obtained from step (ii) with a gas mixture consisting of hydrogen and oxygen or air or O.sub.2 enriched air in an aqueous reaction medium, comprising a mineral acid at the following reaction conditions: concentration of mineral acid in the reaction medium above 0.001 mol/dm.sup.3, concentration of the solid catalyst in the reaction medium above 0.01 g/dm.sup.3, H.sub.2/O.sub.2 mole ratio in the gas mixture in the range from 0.01 to 10, flow rate of the gas mixture in the range from 50 cm.sup.3/g catalyst/h to 50,000 cm.sup.3/g catalyst/h, gas pressure at least 0.9 atm, and temperature below 100.degree. C. and contact period of the reaction medium at least 0.01 h, is disclosed.