NOVELTY - Producing a lithium ion secondary battery (1) comprises: selecting a positive electrode active material that has a prescribed specific surface area; preparing a non-aqueous electrolyte solution (8) that contains lithium difluorophosphate (I) at a prescribed concentration; fabricating a battery in which the non-aqueous electrolyte solution and an electrode assembly (5) are housed in a battery case (6), where the electrode assembly has a positive electrode (2) that contains the positive electrode active material; and activating the battery.    USE - The method is useful for producing a lithium ion secondary battery (claimed) which is used as power sources for mobile, portable devices, electric automobiles and hybrid automobiles.    ADVANTAGE - The method provides the lithium ion secondary battery with high output (preferably excellent low-temperature output), and improved inhibition of heat generation (preferably heat generation during overcharging).    DETAILED DESCRIPTION - Producing a lithium ion secondary battery (1) comprises: selecting a positive electrode active material that has a prescribed specific surface area; preparing a non-aqueous electrolyte solution (8) that contains lithium difluorophosphate of formula (I) at a prescribed concentration; fabricating a battery in which the non-aqueous electrolyte solution and an electrode assembly (5) are housed in a battery case (6), where the electrode assembly has a positive electrode (2) that contains the positive electrode active material; and activating the battery, where, in an xy-coordinate plane that gives a relationship between a specific surface area (x (m2/g)) of the positive electrode active material and a concentration (y (mole/kg)) of (I) in the non-aqueous electrolyte solution, a combination of the prescribed specific surface area and the prescribed concentration corresponds to a combination of values that lies within a hexagonal inner region formed by connecting 6 points i.e. (x, y) is (0.80, 0.035), (2.20, 0.05), (2.60, 0.10), (2.60, 0.16), (0.80, 0.16), and (0.50, 0.10) in this sequence with straight lines. An INDEPENDENT CLAIM is also included for a lithium ion secondary battery comprising an electrode assembly having a positive electrode that contains a positive electrode active material that has a prescribed specific surface area, a non-aqueous electrolyte solution that contains (I) at a prescribed concentration, and a battery case.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic view of the lithium ion secondary battery.    Lithium ion secondary battery (1)    Positive electrode (2)    Electrode assembly (5)    Battery case (6)    Non-aqueous electrolyte solution (8)