ESCRT-III proteins catalyze membrane fission during multi vesicular body biogenesis, budding of some enveloped viruses and cell division. We suggest and analyze a novel mechanism of membrane fission by the mammalian ESCRT-III subunits CHMP2 and CHMP3. We propose that the CHMP2-CHMP3 complexes self-assemble into hemi-spherical dome-like structures within the necks of the initial membrane buds generated by CHMP4 filaments. The dome formation is accompanied by the membrane attachment to the dome surface, which drives narrowing of the membrane neck and accumulation of the elastic stresses leading, ultimately, to the neck fission. Based on the bending elastic model of lipid bilayers, we determine the degree of the membrane attachment to the dome enabling the neck fission and compute the required values of the protein-membrane binding energy. We estimate the feasible values of this energy and predict a high efficiency for the CHMP2-CHMP3 complexes in mediating membrane fission. We support the computational model by electron tomography imaging of CHMP2-CHMP3 assemblies in vitro. We predict a high efficiency for the CHMP2-CHMP3 complexes in mediating membrane fission.