NOVELTY - Lithium-manganese complex oxide active material having specified Li/Mn atomic ratio, lattice constant, half-width value and average primary particle size is used as positive electrode active material. Amorphous carbon material having specified negative electrode density, true density and crystalline thickness is used as negative electrode active material.    USE - For electric power storage systems, electric vehicles, elevator power source, electric tools, etc..    ADVANTAGE - Has longer high-temperature life than conventional batteries, and has high input and output characteristics.    DETAILED DESCRIPTION - The lithium secondary battery comprises a negative electrode, a non-aqueous electrolyte, and a positive electrode.    The negative electrode active material comprises amorphous carbon whose negative electrode density is more than 0.95 g/cc and less than 1.5 g/cc.    The positive electrode active material comprises a complex oxide material including Li and Mn, which has a spinel-type crystalline structure, and a half width value of 2 theta angle of peak (400) in X-ray diffraction pattern smaller than 0.20 degrees.    The Li/Mn ratio of the complex oxide is above 0.55 and less than 0.80. The lattice constant of the spinel crystalline structure of the complex oxide is above 8.031 Angstrom and less than 8.230 Angstrom.    The specific surface area of secondary particles of the complex oxide is above 0.10 square meters/g and less than 1.5 square meters/g. The average particle diameter of primary particles of the complex oxide is above 1 microns and less than 20 microns.    A single battery of this type has input density 300-1800 W/kg, and output density 500-3500 W/kg, and operating temperature in the range -10 to 50 degrees C.    Two INDEPENDENT CLAIMS are given for lithium secondary batteries, where, respectively:    (a) the true density of amorphous carbon comprising the negative electrode active material is 1.2-1.8 g/cc; and    (b) the crystalline thickness of amorphous carbon comprising the negative electrode active material is 5-150 Angstrom.    DESCRIPTION OF DRAWING(S) - The drawing shows a partially sectional side view of the lithium secondary battery of an embodiment according to the invention.    Negative electrode (2)    Positive electrode (3)    Battery can (4)    Insulating member (5)    Positive electrode terminal (6)    Negative electrode terminal (7)