A method of recovering in highly pure states heavy metals such as cobalt, manganese, etc., and bromine without the contamination of organic impurities and heavy metal impurities from the residue of the reaction mother liquor, which is obtained by removing a solvent from the reaction mother liquor remained after recovering terephthalic acid from the oxidation reaction product obtained in the method of producing terephthalic acid by subjecting an alkylbenzene such as p-xylene to a liquid phase oxidation with oxygen or oxygen-containing gas in the presence of a catalyst containing the heavy metals and bromine using a lower aliphatic monocarboxylic acid as the solvent, said method comprising: stirring the residue of the reaction mother liquor with water as solvent in the presence of molecular oxygen and a sulfur compound, removing solid impurities from the extracted mixtures thus treated by solid-liquid separation to provide an aqueous catalyst extract solution, passing the aqueous solution through a column packed with a strongly acidic cation-exchange resin to adsorb thereon the heavy metal catalyst, distilling the solution thus passed through the ion-exchange resin to recover bromine contained in the aqueous extract solution as hydrobromic acid, and, on the other hand, passing hydrobromic acid through the column of the ion exchange resin having adsorbed thereon the heavy metal catalyst to desorb the heavy metal catalyst, whereby the heavy metal catalyst is recovered as the bromide of it.