NOVELTY - The non-aqueous electrolyte secondary battery comprises a positive electrode (1) having lithium-transition metal composite oxide containing manganese as a transition metal, and a negative electrode (4) for leaving lithium ion. The positive electrode and negative electrode are represented in a non-aqueous electrolyte solution. The non-aqueous electrolyte solution is obtained by dissolving phosphoric acid ester amide (I) and an electrolyte in a non-aqueous solvent. The non-aqueous electrolyte contains a cyclic carbonate or linear carbonate as a solvent.    USE - Non-aqueous electrolyte secondary battery, preferably lithium secondary battery used as power supply for tablet computer, cellular phones, notebook computers, and for use in large sized electrical storage, such as power supply for electric power storage and electric vehicles.    ADVANTAGE - The non-aqueous electrolyte secondary battery shows a high output density and a high energy density with reduced carbon-dioxide emission, suppresses manganese elution from a positive electrode and a high temperature preservation, and improves charging/discharging cycling characteristics in high temperature.    DETAILED DESCRIPTION - The non-aqueous electrolyte secondary battery comprises a positive electrode having lithium-transition metal composite oxide containing manganese as a transition metal, and a negative electrode for leaving lithium ion. The positive electrode and negative electrode are represented in a non-aqueous electrolyte solution. The non-aqueous electrolyte solution is obtained by dissolving phosphoric acid ester amide of general formula (I) and an electrolyte in a non-aqueous solvent.    m and (3-m)=1-2; and    R1-R3=represents hydrocarbon group which has linear or branched 1-20C saturated hydrocarbon or an unsaturated bond, which may be substituted with a substituent selected from alkoxy group, amino group, alkylthio group, halogen atom, saturated heterocyclic group or unsaturated heterocyclic group.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic cross-sectional view of the lithium secondary battery.    Positive electrode (1)    Positive electrode stainless steel cap (2)    Negative electrode stainless steel cap (3)    Negative electrode (4)    Stainless steel plate spring (5)