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This paper proposes a new approach to converting irregular genus-0 meshes into those with subdivision connectivity. The original mesh is parameterized onto the unit sphere firstly. Then a spherical base mesh is constructed with only four vertices. After that, a 1-to-4 subdivision operation and an iterative vertex relocation operation are applied alternately over the base mesh to produce a spherical subdivision mesh, which has similar vertex distribution as the spherical parameterized one. Finally, the remesh with subdivision connectivity is obtained by sampling the original surface. The experimental results show that our method can not only make the number of irregular vertices in the remesh as small as possible (only four), but also preserve the details of original model well.