The thermal stability of ultrasmall 0.4nm single-walled carbon nanotubes (SWNTs) are studied by means of Raman-scattering measurements under a vacuum. The 0.4nm SWNTs are very stable when they are confined inside the channels of the AlPO4-5 zeolite crystal. When these SWNTs are extracted from the channels into free space, however, they become thermally unstable because of the strong curvature effect. The in situ Raman-scattering measurement under 1×10-5mbar shows all three structures of the 0.4-nm-sized SWNTs are destroyed between 730to790K, a temperature range much lower than that of large-sized SWNTs. The (5,0) tube is only destroyed after the temperature reaches 790K and seems slightly more stable than the other two structures: the (3,3) and (4,2) tubes. A reference measurement under UHV conditions confirms that the 0.4nm SWNTs are destroyed after the same thermal treatment indicating that the structural degradation is determined by the curvature effect other than oxidation. © 2005 The American Physical Society.