Decomposition process of the Al-Cu-Co single quasicrystals (falling apart into small pieces) after annealing at 100°C for 20 h was studied by X-ray topography, high-resolution electron microscopy, X-ray diffractometry and optical microscopy. It was found that the decomposition of the single quasicrystals is preceded by the creation of a large number of antiphase microdomains and the deformation of the clusters occurs in the two-fold directions of [01100] type. The decomposition begins with the propagation of cracks in the directions of [01100] type.