The stability of single-crystalline icosahedral Cd-Yb was investigated using X-ray diffraction methods in the temperature range 20 K ≤ T ≤ 900 K at ambient pressure and from ambient temperature to 873 K at about 9 GPa. Single-crystals remain stable at low temperatures and in the investigated HP-HT-regime. At high temperatures and ambient pressure, the quasicrystal decomposes. The application of mechanical stress at low temperatures yields to the same decomposition, the formation of Cd. A reaction of icosahedral Cd-Yb with traces of oxygen or water causing the decomposition seems reasonable, but a low-temperature instability of this binary quasi-crystal cannot be ruled out totally.