A composite oxide synthesized by a citrating process and utilized in functional ceramics materials is prepared by the following process. Co-precipitants or mixtures of at least one component selected from the group consisting of carbonates, basic copper and/or hydroxides of elements which compose a composite oxide are reacted with citric acid in an aqueous solution or in an organic solvent. The elements are selected from at least one element of the group consisting of Y, rare earth elements, transition elements, and alkali metal or alkaline earth metal elements. The citrate compound formed is baked to complete the composite oxide.The composite oxide synthesized by this invention has superconduction at the most temperature of 93.degree. K. with excellent Meissner effect.