TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The phosphate compound comprises at least one element comprising neodymium, samarium, europium, erbium, ytterbium or lutetium. The ratio of the phosphate compound on an elemental neodymium, samarium, europium, erbium, ytterbium, or lutetium, relative to the positive electrode active material is 0.01-0.25 mass%. The positive electrode active material is a lithium transition metal oxide having a layered structure. In the method, the phosphate is at least one of disodium hydrogen phosphate dodecahydrate, ammonium dihydrogen phosphate, diammonium hydrogen phosphate, sodium dihydrogen phosphate, phosphoric acid anhydride, phosphoric acid, lithium phosphate, and potassium phosphate. Preferred Method: In the method, coating the surface of the positive electrode active material with the surface treatment layer comprises adding acid or base to the solution containing the positive electrode active material, to control pH of the solution 2-7. EXAMPLE - Lithium cobaltate (500 g), which was a positive electrode active material, was added to pure water (3 l) and the mixture was stirred. An aqueous solution obtained by dissolving disodium hydrogen phosphate dodecahydrate (0.77 g) and neodymium nitrate hexahydrate (0.9 g) was added to the mixture being stirred to deposit neodymium phosphate on the surface of lithium cobaltate. Nitric acid (10 mass%) and sodium hydroxide solution (10 mass%) were added to the resultant solution to keep pH of the solution at 6.5. The resultant mixtures were filtered and washed with water. The resultant powder was dried at 120 degrees C and then fired in the air at 300 degrees C for 5 hours to obtain lithium cobaltate having a surface treatment layer composed of neodymium phosphate formed on the surface of it. The neodymium phosphate (0.059 mass%) was attached to lithium cobaltate on an elemental neodymium basis. The positive electrode active material, acetylene black, and polyvinylidene fluoride were mixed so as to have a mass ratio of 95:2.5:2.5. The resultant mixture was kneaded together with N-methyl pyrrolidone to prepare positive electrode active material slurry. The positive electrode active material slurry was applied to both sides of a positive electrode current collector composed of aluminum foil, and drying and rolling were performed to obtain a positive electrode. Graphite serving as a negative electrode active material, styrene-butadiene rubber, and carboxymethyl cellulose were mixed so as to have a mass ratio of 98:1:1. The resultant mixture was kneaded in an aqueous solution to prepare negative electrode active material slurry. The negative electrode active material slurry was applied to both sides of a negative electrode current collector composed of copper foil, and drying and rolling were performed to obtain a negative electrode. Lithium hexafluorophosphate was added to a solvent obtained by mixing ethylene carbonate and diethyl carbonate at a volume ratio of 3:7, so that the lithium hexafluorophosphate concentration was 1 mol/l. Furthermore, vinylene carbonate was added to the solvent in a concentration of 1 mass% relative to the solvent, to obtain a non-aqueous electrolyte. After lead terminals were attached to the positive electrode and the negative electrode, the positive electrode and the negative electrode were wound with a separator in between them. The wound body was pressed into a flat shape, where an electrode body was prepared. The electrode body was inserted into an aluminum laminate serving as a battery casing and then the non-aqueous electrolyte was injected into the aluminum laminate to produce a test battery.