The culminating step of the intraerythrocytic development of Plasmodium falciparum, the causative agent of malaria, is the spectacular release of multiple invasive merozoites on rupture of the infected erythrocyte membrane. This work reports for the first time that the whole process, taking place in time scales as short as 400 milliseconds, is the result of an elastic instability of the infected erythrocyte membrane. Using high-speed differential interference contrast (DIC) video microscopy and epifluorescence, we demonstrate that the release occurs in 3 main steps after osmotic swelling of the infected erythrocyte: a pore opens in ~ 100 milliseconds, ejecting 1-2 merozoites, an outward curling of the erythrocyte membrane is then observed, ending with a fast eversion of the infected erythrocyte membrane, pushing the parasites forward. It is noteworthy that this last step shows slight differences when infected erythrocytes are adhering. We rationalize our observations by considering that during the parasite development, the infected erythrocyte membrane acquires a spontaneous curvature and we present a subsequent model describing the dynamics of the curling rim. Our results show that sequential erythrocyte membrane curling and eversion is necessary for the parasite efficient angular dispersion and might be biologically essential for fast and numerous invasions of new erythrocytes.