NOVELTY - A non-aqueous electrolyte secondary battery comprises a positive electrode having a positive electrode active material layer containing active material (e.g. cobalt and/or magnesium); a polymer layer formed on a surface of the active material layer; a negative electrode; a separator between the electrodes; an electrode assembly and a non-aqueous electrolyte. The positive electrode has an end-of-charge potential of 4.4 V versus potential of a lithium reference electrode. The polymer layer is composed of a polymer having a partially cross-linked structure and molecular weight of greater than or equal to 800000.    USE - As non-aqueous electrolyte secondary battery such as lithium-ion batteries useful for driving power sources for mobile information terminals such as mobile telephones, notebook computers, and personal digital assistants (PDAs), especially for use in applications that require a high capacity; and for high power applications that require continuous operations under high temperature conditions, such as hybrid electrical vehicles (HEVs) and power tools, in which the battery operates under severe operating environments.    ADVANTAGE - The battery structure is excellent in cycle performance and storage performance under high-temperature conditions and exhibits high reliability even with a high power battery design. The polymer layer provided on the surface of the positive electrode active material layer properly exhibits a filtering function. Thus, the polymer layer traps the decomposition products of the electrolyte solution resulting from the reaction at the positive electrode as well as the cobalt or manganese ions dissolved away from the positive electrode active material, preventing the cobalt or manganese from depositing on the negative electrode and the separator. As a result, damage to the negative electrode and the separator is alleviated, and therefore, an excellent advantageous effect is exhibited that deterioration in the cycle performance under high temperature conditions and deterioration in the storage performance under high temperature conditions can be lessened. The polymer layer disposed on the surface of the positive electrode active material layer properly exhibits a filtering function. Thus, the polymer layer traps the decomposition products of the electrolyte solution resulting from the reaction at the positive electrode as well as the cobalt or manganese ions dissolved away from the positive electrode active material, preventing the cobalt or manganese from depositing on the negative electrode and the separator. This makes it possible to alleviate damage to the negative electrode and the separator. Therefore, it is possible to lessen deterioration in the cycle performance under high temperature conditions and deterioration in the storage performance under high temperature conditions. Moreover, since the polymer layer is disposed on the surface of the positive electrode active material layer, not on the surface of the positive electrode active material particles (i.e. the polymer layer is coated over a large area), it is not difficult to control the thickness of the polymer layer. As a result, it is possible to prevent an increase in the internal resistance of the battery resulting from a polymer layer with a large thickness. Raising the end-of-charge voltage of positive electrode to 4.4 V accomplishes about a 10% increase in the overall battery capacity. When positive electrode active material layer has a filling density of greater than or equal to 3.40 g/cc, the reaction in the positive electrode takes place over the entire electrode, not locally. Therefore, the deterioration of the positive electrode also proceeds uniformly and does not significantly affect the charge-discharge reactions after storage.    DETAILED DESCRIPTION - A non-aqueous electrolyte secondary battery comprises a positive electrode having a positive electrode active material layer comprising a positive electrode active material containing at least cobalt or manganese; a polymer layer formed on a surface of the positive electrode active material layer; a negative electrode having a negative electrode active material; a separator interposed between the positive electrode and the negative electrode; an electrode assembly comprising the positive electrode, the negative electrode, and the separator; and a non-aqueous electrolyte impregnated in the electrode assembly. The positive electrode having an end-of-charge potential of 4.40 V versus the potential of a lithium reference electrode. The polymer layer is composed of a polymer having a partially cross-linked structure and a molecular weight of greater than or equal to 800000. The polymer layer has a mass of less than or equal to 3.3x10-4 g/cm2 per unit area of the positive electrode-active material layer. The product of separator thickness x (microns) and separator porosity y (%) is less than or equal to 1500 (preferably less than or equal to 800) microns%. The positive electrode active material layer has a filling density of greater than or equal to 3.40 g/cc.