We calculate the surface energy of a micelle consisting of neutral and ionized dodecyldimethylamine oxides (DDAOs) by Monte Carlo simulation based on a lattice model of the micelle. We obtain the dependence of the surface energy on the fraction alpha(M) of ionized DDAO, the concentration C-S, of salt in an aqueous solution and temperature T. We show that the hydrogen bond between DDAOs plays a significant rule in determining the properties of micelles. In order to explain experiments, a DDAO molecule on the micelle surface is assumed to support two hydrogen bonds. We show that the continuous chain of the hydrogen bonds will be made on the surface in equilibrium. The surface energy takes its minimum at a specific value alpha(M)* of the concentration of ionized DDAO and alpha(M)* is shown to be an increasing function of C-S and a decreasing function of T.