TECHNOLOGY FOCUS - ELECTRICAL POWER AND ENERGY - Preferred Property: The lithium secondary battery is currently designed such that the charging electric potential of the positive electrode in a full-charge state is 4.4 V or more (vs. Li/Li+).    TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Composition: A compound containing molybdenum, tungsten, niobium, tantalum and/or rhenium is also used as raw material. The addition amount of compound containing arsenic, germanium, phosphorus, lead, antimony, silicon and/or tin is 0.05-5 mol% with respect to the total amount of raw material. In the surface portion of primary particles, the ratio of lithium and sum total of arsenic, germanium, phosphorus, lead, antimony, silicon and tin is 1-200 times of the atomic ratio of the particles. The powder further contains a compound containing boron and/or bismuth. The lithium-transition metal type compound is lithium-nickel-manganese-cobalt type having a layered structure or lithium-manganese composite oxide having a spinel structure. The lithium-nickel-manganese-cobalt composite oxide is of formula: Li1+xMO2 or Li(LiaM'bMn2-b-a)O4+d. The molar ratio of manganese and nickel is 0.1-5, the molar ratio of cobalt with respect to the total content of manganese, nickel and cobalt is 0-0.35, and the molar ratio of element (M) and lithium is 0.001-0.2.x=0-0.5;M=Li, Ni, Mn and/or Co;a=0-0.3;b=greater than 0.4 and less than 0.6;d=greater than -0.5 and less than 0.5;andM'=Ni, Cr, Fe, Co, Cu, Zr, Al and/or Mg.Preferred Properties: The powder X-ray diffraction measurement using CuK alpha -ray of the powder shows that FWHM is 0.01-0.5 when the half-value width and full width at half maximum (FWHM) of the diffraction peak near 64.5 degrees is present in the diffraction angle 2 theta . Preferred Conditions: Pulverization is carried out until the median diameter is 0.7 mu m or less. The slurry is spray-dried under the conditions which satisfy the relationships given by, V = 50-10000 cP and G/S is 500-10000, where V is viscosity, S is slurry feed rate (L/min), and G is gas supply volume (L/min). The median diameter is measured after ultrasonic dispersion at an output of 30 W with a frequency of 22.5 kHz for 5 minutes, using a laser diffraction/scattering type particle size distribution measuring apparatus. The refractive index is set to 1.24, and the median diameter is measured by making particle-diameter reference into volume basis.