The recently developed corona above water technique is applied to water containing 10 mg l-1 methylene blue (MB) or methyl orange (MO). The corona discharge pulses are created with a spark gap switched capacitor followed by a transmission line transformer. The pulse amplitude is 40 kV; its duration is 50 ns. At a pulse repetition rate of 10 Hz this leads to an average power of 0.6 W into the discharge. MB and MO are completely decolourized in ~20 min. This corresponds to a yield of ~4.5 gr kW-1h-1, which is much higher than obtained with other discharge techniques or sonoluminescence. The high yield is reflected in the observed temperature increase of only ~1 K. Tests with additional chemicals show that the initial speed of the conversion can be influenced but the total time required for total decolourization is constant. Further, it follows that the main oxidation path of the dyes is by direct ozone attack and the conversion products are strong acids.