NOVELTY - A lithium ion secondary cell comprises positive electrode and negative electrode, provided through non-aqueous electrolyte solution. The positive electrode contains lithium-magnesium-nickel-containing complex oxide (1). The non-aqueous electrolyte solution contains keto-containing anion compound (2) and electrolyte having lithium hexafluorophosphate as main component in mixed organic solvent containing 10-40 volume% of dimethyl carbonate.    USE - Lithium ion secondary cell is used for electric vehicles and information communication apparatus such as personal computer and mobile telephone.    ADVANTAGE - The lithium ion secondary cell has favorable charging/discharging cycle characteristics.    DETAILED DESCRIPTION - A lithium ion secondary cell comprises positive electrode and negative electrode, provided through non-aqueous electrolyte solution. The positive electrode contains lithium-magnesium-nickel-containing complex oxide of formula: LitMgxNiyMezO2 (1). The non-aqueous electrolyte solution contains keto-containing anion compound (2) and electrolyte having lithium hexafluorophosphate as main component in mixed organic solvent containing 10-40 volume% of dimethyl carbonate.    t=0.8-1.3;    x=0.01-0.2;    y=0.6-0.98;    z=0.01-0.2, where sum of x, y and z is 1;    M=transition element, 13 group, 14 group or 15 group element of periodic table;    b=1-3;    m=1-4;    n=0-8;    q=0-1;    R1=1-10C alkylene, 1-10C haloalkylene, 6-20C arylene or 6-20C haloarylene, where alkylene and arylene have substituent and heteroatom;    R2=halo, 1-10C alkyl, 1-10C alkylhalide, 6-20C aryl and 6-20C haloaryl, or -X3R3 where alkyl and aryl optionally have substituent and heteroatom;    X1-X3=oxygen, sulfur or NR4;and    R3,R4=H, 1-10C alkyl, 1-10C alkyl halide, 6-20C aryl and 6-20C halo aryl, where alkyl and aryl optionally have substituent and heteroatom, R3 and R4 optionally bonded to form ring.    When q is 1 and m is 2-4, R1 bonded to form ring, and when n is 2-8, R2 optionally bonded to form ring.