TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The lithium-containing transition metal oxide includes a domain, where: nickel and manganese are contained in a molar ratio of 1:1 or 2:1; and nickel and cobalt are contained in a molar ratio of 1:1. In (A), a triangular phase diagram shows the element contents of nickel, manganese, and cobalt in terms of molar ratio, where (I) falls within a pentagonal region defined by five vertices satisfying x:y:z is equal to 6:2:2, 5:2.5:2.5, 5:3.3:1.7, 6.36:2.73:0.91, and 6.25:2.5:1.25. While performing charge and discharge using (A), which is formed into a sheet, at a current density of 0.33 mA/cm2 or less per unit area of the sheet and 8 mA/g or less per unit weight of (A) and at a potential of 4.3-3 V versus lithium metal potential, where the difference between a charge capacity at the first cycle and a discharge capacity at the third cycle (irreversible capacity) is 20 mAh/g or less, and the reversible capacity at the third cycle is 165 mAh/g or more. The lithium-containing transition metal oxide includes a secondary particle having an average particle size (D50) of 11 mu m or less, where the secondary particle is a sintered body of primary particles having an average particle size (D50) of 2 mu m or less. The tap density of the lithium-containing transition metal oxide is 2 (preferably 2.2) g/cm3 or more. The potential at which potential V sharply drops in a final stage of discharge (the potential that gives a maximum d3 Q/dV3 by triple differentiation when capacity is denoted by Q) is higher than 3.45 V versus lithium metal. While performing a differential scanning calorimetry (DSC) at temperature elevation rate of 10 degrees C/minutes after charging up to 4.4 V as a potential versus lithium metal, no substantial exothermic peak appears at 200 degrees C or less temperature. The interior or the surface of the primary particles is doped with a different element comprising aluminum, magnesium, zirconia, manganese and/or tin. The negative electrode includes a carbonaceous material capable of absorbing and desorbing lithium. Preferred Method: The temperature in the baking is higher than 800 degrees C, preferably 900 degrees C or higher. EXAMPLE - Precursor with high tap density was synthesized by a coprecipitation method. In this process, the feeding rate of each aqueous sulfuric acid solution was adjusted to obtain target composition of nickel, manganese, and cobalt. To the obtained precursor, lithium carbonate was added so that the ratio (molar ratio) of lithium/Me (where the Me was transition metal elements) was 0.03. The resultant mixture was baked at 935 degrees C for 10 hours to give an active material having the target composition (5/2.5/2.4). The samples after baking were pulverized with a jet mill to give active material particles. The particle size of the active material particles were greatly influenced by the particle size of the precursor. The particle size of the precursor was controlled by the conditions of coprecipitation.