Methane oxidative coupling in the presence of the catalyst 1% Au/5% La2O3/CaO and gas-phase initiator hydrogen peroxide at the temperature 700-800 degrees C under normal pressure has been studied. It has been shown that hydrogen peroxide remarkably increases the yield of C-2+ products without the loss of selectivity. The maximal yield of C-2+ products under the conditions studied was 27% with the formation of a noticeable quantity of benzene. It has been proposed, that the observed effect is due to hydroxyl radical formation from hydrogen peroxide, which could be essential under definite conditions also in a conventional catalytic methane oxidative coupling.