NOVELTY - An alkaline solution is added to mixed aqueous solution of nickel salt and metallic element salt, and hydroxide of nickel and metallic element are coprecipitated. The obtained deposit is filtered, washed with water and dried, to obtain nickel composite hydroxide (I). The obtained nickel composite hydroxide and lithium compound are mixed, such that molar ratio of lithium with respect to total of nickel and metal (M) is 1-1.15. Resultant mixture is baked at 700-1000 degrees C, and water-washed, to form lithium-nickel complex oxide (II), and to obtain positive electrode active material.    USE - Manufacture of positive electrode active material used for nonaqueous electrolyte secondary battery e.g. 2032-type coin battery (all claimed) and lithium-ion battery used as power supply for small-and-large-sized portable electronic device e.g. mobile telephone and notebook computer, electric vehicle and hybrid vehicle e.g. hybrid car.    ADVANTAGE - The battery containing the positive electrode active material has favorable thermal stability, and charging and discharging characteristics.    DETAILED DESCRIPTION - An alkaline solution is added to mixed aqueous solution of nickel salt and metallic element salt, and hydroxide of nickel and metallic element are coprecipitated. The obtained deposit is filtered, washed with water and dried, to obtain nickel composite hydroxide of formula: NixM1-x(OH)2 (I). The obtained nickel composite hydroxide and lithium compound are mixed, such that molar ratio of lithium with respect to total of nickel and metal is 1-1.15. Resultant mixture is baked at 700-1000 degrees C and water-washed, to form lithium-nickel complex oxide of formula LiNixM1-xO2 (II), and to obtain positive electrode active material.    (4-Z)x=0.75 or more;    Z=average valence of nickel;and    M=additional element(s) whose average valence as whole is 3.375 or more.    DESCRIPTION OF DRAWING(S) - The drawing shows a sectional view of the battery containing the positive electrode active material. (Drawing includes non-English language text)    Positive electrode (1)    Negative electrode (2)    Separator (3)    Gasket (4)    Coin battery (B)