TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preparation (Claimed): Preparation of the zirconium oxide hydrate particles involves: adding an aqueous zirconium salt solution to an aqueous alkaline solution while controlling a pH to 7-13, and subjecting the zirconium oxide hydrate particles to a hydrothermal treatment in the presence of water at a temperature of 50-110 degrees C for 3 hours. The method further involves: aging the aqueous solution in which the zirconium oxide hydrate particles are prepared at a pH of 7-13 at 20-90 degrees C for 5-40 hours; drying the zirconium oxide hydrate particles subjected to a hydrothermal treatment in air at a temperature of 20-90 degrees C for 3-12 hours. The aging step is carried out prior to the step of a hydrothermal treatment. Preferred Particles: The zirconium oxide hydrate particles have a mean primary particle size of 1-3.5 nm. Preferred Definitions:    n= greater than or equal to 4.    EXAMPLE - Aqueous ammonia solution was prepared by mixing 28% aqueous ammonia solution (15.12 g) with water (300 ml). Separately from this aqueous ammonia solution, an aqueous zirconium salt solution was prepared by dissolving zirconium oxychloride octahydrate (8 g) in water (100 ml). Next, the aqueous ammonia solution was stirred while the aqueous zirconium salt solution was added dropwise to it, thus generating a precipitate containing zirconium oxide hydrate particles. The aqueous zirconium Bait solution was completely used in this dropwise addition. The pH of the suspension containing this precipitate was 11.8. This precipitate was aged at 25 degrees C for 15 hours in the state of a suspension. The pH of the suspension after 15 hours was 11.3. Then, the suspension containing this precipitate was introduced into an autoclave and subjected to a hydrothermal treatment at 100 degrees C for 4 hours (hydrothermal treatment step). Finally, after water washing was carried out using an ultrasonic cleaner to remove unreacted ingredients and impurities from the precipitate after the hydrothermal treatment, filtration was carried out, and then drying was carried out at 60 degrees C for 6 hours in air according to the standard for the measurement of the amount of hydration described above (drying step). Then, the resultant was lightly crushed using a mortar, and zirconium oxide hydrate particles were obtained. The zirconium oxide hydrate particles had mean primary particle size of 3.2 nm; amount of water of hydration of 5.59.