NOVELTY - A molten material containing metal oxide compound (A) (I), is melted and cooled, to obtain solidified material. The obtained solidified material is pulverized, to obtain ground material containing metal oxide compound (A) (II). The obtained ground material is heated under inert gas or reducing gas, to obtain coated particles coated with electroconductive material. The obtained coated particles are mixed solvent and fluorine-containing polymer, to obtain composition, the solvent in the obtained composition is removed and heated, to obtain positive electrode active material.    USE - Manufacture of positive electrode active material for manufacture of secondary battery (claimed) used for plug-in hybrid motor vehicle and electric vehicle.    ADVANTAGE - The method economically provides positive electrode active material having high productivity and excellent uniformity, by a simple process. The secondary battery manufactured by the positive electrode active material is safe, and has excellent reliability and electrical conductivity.    DETAILED DESCRIPTION - A molten material containing metal oxide compound (A) of formula: AaMbXcOd1Z'e1 (I), is melted and cooled, to obtain solidified material. The obtained solidified material is pulverized, to obtain ground material containing metal oxide compound (A) of formula: AaMbXcOdZe (II). The obtained ground material is heated under inert gas or reducing gas, to obtain coated particles coated with electroconductive material. The obtained coated particles are mixed solvent and fluorine-containing polymer formed by dispersing or melting in the solvent, to obtain composition, the solvent in the obtained composition is removed and heated, to obtain positive electrode active material.    A=lithium, sodium or potassium;    M=iron, manganese, cobalt or nickel;    X=silicon, phosphorus, sulfur, boron, aluminum, vanadium, molybdenum, tungsten, arsenic, germanium or antimony;    Z'=halo;    a=0.8-2.7;    b=0.6-1.4;    c=0.9-1.1;    d1,d=valence of M and valence of X;    e1=0-2.2;and    e=0-e1.    An INDEPENDENT CLAIM is included for manufacture of secondary battery.