There is obtained a material of a positive electrode for a secondary lithium-ion cell having high cycle durability and high safety in high-voltage and high-capacity applications, which is a particulate positive electrode active material for a secondary lithium-ion cell represented by a general formula, Li.sub.aCO.sub.bA.sub.cB.sub.dO.sub.eF.sub.f (A is Al or Mg, B is a group-IV transition element, 0.90.ltoreq.a.ltoreq.1.10, 0.97.ltoreq.b.ltoreq.1.00, 0.0001.ltoreq.c.ltoreq.0.03, 0.0001.ltoreq.d.ltoreq.0.03, 1.98.ltoreq.e.ltoreq.2.02, 0.ltoreq.f.ltoreq.0.02, and 0.0001.ltoreq.c+d.ltoreq.0.03), where element A, element B and fluorine are evenly present in the vicinity of the particle surfaces.