TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Property: Lithium carbonate has a mean particle size of 6 mu m or less. Preferred Components: The transition-metal compound comprises a hydroxide produced by adding an alkali to an aqueous solution of a nickel salt and a salt of metal (M) to co-precipitate nickel and metal (M). Metal (M) includes manganese and/or cobalt. Metal (M) further includes aluminum, magnesium, calcium, strontium, yttrium, ytterbium and/or iron. Preferred Method: The setting of mixture temperature to preset range involves causing the mixture to flow in a rotating cylindrical kiln in which the temperature at one end is lower than the temperature inside, introducing the mixture from the end, and switching the rotation direction of the kiln to the opposite direction several times. The inner face of the kiln has a spiral groove or rib. The kiln is a rotary kiln. The obtained reaction product is further heated in a furnace. Preferred Conditions: The preset temperature range is 550-750 degrees C. The heating temperature in the furnace is 800-1100 degrees C. EXAMPLE - An aqueous solution of nickel sulfate, an aqueous solution of manganese sulfate, and an aqueous solution of cobalt sulfate, having a concentration of 1.2 mol/L, were prepared. These aqueous solutions were introduced into a reaction vessel in a molar ratio (nickel:manganese:cobalt) of 3:1:1. Simultaneously with this, an aqueous solution of 4.8 mol/L sodium hydroxide was introduced. Argon gas was bubbled in the aqueous solution in the reaction vessel to expel dissolved oxygen. A coprecipitation reaction was carried out to obtain a co-precipitated hydroxide of formula: Ni3/5Mn1/5Co1/5(OH)2. The coprecipitated hydroxide was mixed with lithium carbonate having a mean particle size of 6 mu m in a molar ratio of (nickel+manganese+cobalt):lithium of 1:1.03. The mixture was introduced into a rotary kiln having a cylindrical kiln. Specifically, the mixture was introduced from one end of the cylindrical kiln rotating at a rotation speed of 2 rpm, and the rotation direction of the cylindrical kiln was regularly switched to the opposite direction. Air was introduced into the cylindrical kiln. The temperature of cylindrical kiln was controlled so that the temperature of the introduced mixture reached approximately 700 degrees C near the center of the cylindrical kiln. The reaction between hydroxide and lithium carbonate was carried out. The obtained reaction product (lithium-containing transition-metal oxide) was collected from the cylindrical kiln, coarsely crushed, and charged into a ceramic container. This was introduced into a furnace, where it was heated in air at 925 degrees C for 7 hours to enhance the crystallinity. The lithium-containing transition-metal oxide was then broken, preliminarily crushed with a roller, and further pulverized/adjusted to a preset particle size. Thus, a lithium-containing transition-metal oxide of formula: LiNi3/5Mn1/5Co1/5O2 was produced. The oxide provided a positive-electrode active material having a discharge capacity of 175 mAh/g.