NOVELTY - A core particles comprising complex of lithium, element chosen from manganese and aluminum, and element chosen from zirconium, tungsten, titanium, magnesium, tantalum, niobium and molybdenum are stirred. Core particles are mixed with solution (s1) comprising rare-earth element and solution (s2) comprising fluorine-containing compound by dripping solution (s1) and solution (s2) till the amount of rare-earth element added reaches 0.02-0.15 mol% to obtain coated-core particles. The coated-core particles are heated to obtain positive electrode active material.    USE - Preparation of active material used for positive electrode of nonaqueous electrolyte secondary battery (all claimed) e.g. lithium-ion secondary battery used as electric power supply of video tape recorder, mobile phone, notebook personal computer, and electric vehicle.    ADVANTAGE - The nonaqueous electrolyte secondary battery formed using the positive electrode active material has high cycle characteristics at high voltage, high energy density and high charge-discharge capacity. When the charging voltage is heightened, the structural collapse of positive electrode active material occurs from around the time and when the charging voltage reaches 4.3 V, the reactivity between constituent element in the positive electrode active material and the nonaqueous electrolyte is enhanced, and the decomposition of the nonaqueous electrolyte is accelerated.    DETAILED DESCRIPTION - A core particles comprising lithium-transition metal composite oxide of formula: LiaNi1-x-y-zCoxM1yM2zO2 (I), where a is 1-1.5, x and y are 0-0.5, z is 0-0.02, x+y is 0.7 or less, M1 is element chosen from manganese and aluminum, and M2 is element chosen from zirconium, tungsten, titanium, magnesium, tantalum, niobium and molybdenum are stirred. Core particles are mixed with solution (s1) comprising rare-earth element and solution (s2) comprising fluorine-containing compound by dripping solution (s1) and solution (s2) till the amount of rare-earth element added reaches 0.02-0.15 mol% based on the amount of core particles and amount of elemental fluorine added reaches 0.07-0.5 mol% based on the amount of core particles to obtain coated-core particles. The coated-core particles are heated at 500 degrees C or less to obtain positive electrode active material.