Abstract: These methods relate to the preparation of a YBa.sub.2 Cu.sub.3 O.sub.7 -d catalyst for purifying an exhaust gas. The method comprises steps of mixing Y.sub.2 O.sub.3, Ba.sub.2 CO.sub.3 and CuO at a mole ratio of 1:4:6, respectively; grinding the resultant mixture to obtain fine powder having a size of at least 200 mesh; sintering the fine powder at temperature of 800.degree. C. to 900.degree. C. under an atmosphere of oxygen; annealing the fine powder to room temperature; pelletizing the powder to form pellets; grinding the pellets to obtain fine powder having a size of at least 200 mesh; re-sintering the resultant fine powder at a temperature of 800.degree. C. to 920.degree. C.; and re-annealing the fine powder to room temperature.