In the present work, results obtained by differential thermal analysis (DTA) and X-ray diffraction (XRD) confirm [5, 8] that the icosahedral phase (i-phase) is formed by a peritectic reaction. A single i-phase can be obtained after annealing around the compositions Al64Cu24Fe12-Al61.75Cu25.5Fe12.75. For the composition Al62Cu25.5Fe12.5, the XRD lines of the i-phase are narrow whatever the annealing temperature (800-degrees-C or 600-degrees-C). Thus, this result establishes that there exists a single phase domain where the i-phase is perfect (without phasons) and remains stable at 600-degrees-C. A provisional vertical section along the line Al70Cu20Fe10-Al64Cu24Fe12-Al58Cu28Fe14 is proposed and shows the phases that exist in equilibrium at various temperatures in this range of compositions.