TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Material: The material (T1) has a-axis lattice constant of greater than or equal to 0.2865 nm, and has c-axis lattice constant of greater than or equal to 1.42069 nm. In the material (T1), the mole ratio of Li to Me' is 0.9-1.2 (preferably 0.97-1.05, especially 0.98-1.02). The ratio of Li atoms in the Li sites is 98-100%. The material (T1) was prepared by firing a precursor hydroxide and a lithium compound at a temperature of 800-900 degrees C. Preferred Components: The electrolyte comprises a non-aqueous organic solvent and a lithium salt. Preferred Method: In the method, the composite transition element precursor is prepared by reacting Ni source material, Co source material, and Mn source material, and in the case of Ni source material, when a total amount of source materials including Ni source material and impurities is assumed to be 100 wt.%, an amount of Fe impurity in the Ni source material is not greater than 0.002 wt.%, and an amount of Co impurity in the Ni source material is not greater than 0.001 wt.%; in the case of the Co source material, when a total amount of source materials including Co source material and impurities is assumed to be 100 wt.%, an amount of Fe in the Co source material is not greater than 0.0005 wt.%, an amount of Cu impurity in the Co source material is not greater than 0.0003 wt.%, an amount of Si impurity in the Co source material is not greater than 0.0025 wt.%, and an amount of Na impurity in the Co source material is not greater than 0.0015 wt.%; and in case of the Mn source material, when a total amount of source materials including Mn source material and impurities is assumed to be 100 wt.%, an amount of Fe impurity in the Mn source material is not greater than 0.0005 wt.%, an amount of Ca impurity in the Mn source material is not greater than 0.01 wt.%, an amount of Na impurity in the Mn source material is not greater than 0.01 wt.%, and an amount of K impurity in the Mn source material is not greater than 0.01 wt.%. In the step (b1), the mixture is placed at 40-70 vol.%. Preferred Definitions:    x=0.55-0.65;    z=0.15-0.25.    EXAMPLE - No suitable example given.