TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Composition: The heat-resistant inorganic complex oxide has a composition expressed as: (Ti)a(Zr)b(alpha)c(Al)dOx.a = 0.01-0.2 (preferably 0.01-0.09);b = 0.01-0.2, (preferably 0.01-0.06);c = 0.01-0.2, (preferably 0.1-0.2);d = 2-a-b-c;x = oxygen number which satisfies stoichiometry;alpha = alkaline earth metal atom.The base material has X-ray diffraction pattern after supporting the catalytically active component, at the time of performing durability test, displayed in table (B).The heat-resistant inorganic complex oxide preferably has composition containing titanium-zirconium-aluminum oxide expressed as: (Ti)a(Zr)b(Al)cOxa = 0.02-0.09;b = 0.01-0.07;c = 2-a-b;x = oxygen number which satisfies stoichiometry.Preferred Method: The water-soluble titanium salt, zirconium acetate and alkaline earth metal salt are impregnated into alumina, and baked to obtain the base material.The water-soluble titanium salt and zirconium acetate are co-impregnated into alumina.Preferred Salt: The water-soluble titanium salt is ammonium salt of oxalic acid.Preferred Conditions: Baking is performed at 900-1000 degrees C, preferably 900-950 degrees C for 1-3 hours, preferably 2-3 hours, in airflow conditions.Preferred Components: The catalytically active components are at least one type of noble metals chosen from platinum, rhodium and palladium. EXAMPLE - Titanium oxalate ammonium solution containing titanium atom (0.01 atoms), and zirconium acetate solution containing zirconium atom (0.19 atoms), were impregnated into oxidized aluminum powder containing aluminum (2 atoms). Subsequently, the impregnated material was dried at 150 degrees C in airflow for 20 hours, and ground. The ground material was baked at 900 degrees C in airflow for 3 hours, and a base material for catalyst supporting was obtained. An exhaust gas purification catalyst supported with noble metals was produced using the base material. The base material had excellent heat-resisting property and durability.