NOVELTY - A slurry obtained by pulverize-mixing a raw material containing a lithium source and an element chosen from manganese, nickel, cobalt, magnesium, iron, aluminum and chromium in a solvent is dried to obtain a precursor. The precursor is baked at 900 degrees C or less, to obtain calcined material. A sintering aid containing element chosen from boron, phosphorus, chlorine, lead, antimony, silicon and vanadium, is mixed with calcined material, to obtain a mixture. The obtained mixture is molded and baked, to obtain sintered compact containing lithium complex oxide (I) as a main component.    USE - Manufacture of mixture used for forming sintered compact used as positive electrode of all-solid-state lithium-ion battery (all claimed). Uses include but are not limited to mobile telephone, pumped hydroelectric storage, small computer, electric power storage and electric vehicles.    ADVANTAGE - The positive electrode formed using the mixture has low heterogenous-phase generation degree and porosity, and provides all-solid-state lithium-ion battery with excellent battery performance.    DETAILED DESCRIPTION - A slurry obtained by pulverize-mixing a raw material containing a lithium source and an element chosen from manganese, nickel, cobalt, magnesium, iron, aluminum and chromium in a solvent is dried, to obtain a precursor. The precursor is baked at 900 degrees C or less, to obtain calcined material. A sintering aid containing element chosen from boron, phosphorus, chlorine, lead, antimony, silicon and vanadium, is mixed with calcined material, to obtain a mixture. The obtained mixture is molded and baked, to obtain sintered compact containing lithium complex oxide of formula: Li(x+y)M1(2-y-p)M2pO(4-a) (I) as a main component. The obtained sintered compact is used as at least one potion of all-solid-state lithium-ion battery positive electrode.    M1=element chosen from Mn, Ni, Co, Mg, Fe, Al or Cr;    M2=element chosen from B, P, Cl, Pb, Sb, Si or V;    x=1-2;    y=0-0.2;    p=more than 0 and 1 or less;and    a=0-1.    INDEPENDENT CLAIMS are included for the following:    (1) manufacture of all-solid-state lithium-ion battery positive electrode; and    (2) all-solid-state lithium-ion battery, which has the positive electrode, a negative electrode, and a solid electrolyte.