We investigate whether the observed high number of carbon- and nitrogen-enhanced extremely metal-poor stars could be explained by peculiar evolutionary properties during the core He flash at the tip of the red giant branch. For this purpose we compute a series of detailed stellar models expanding upon our previous work; in particular, we investigate if during the major He flash the penetration of the helium convective zone into the overlying hydrogen-rich layers can produce carbon- and nitrogen-rich abundances in agreement with current spectroscopic observations. The dependence of this phenomenon on selected model input parameters, such as initial metallicity and treatment of convection is examined in detail.