Superconducting oxide REBa₂Cu₄O₈ (RE124; RE=Y, Sm, Eu, Gd, Dy, Ho, Er, Tm and Yb) were synthesized by a molten hydroxide method under an ambient pressure. Rare earth oxide, barium carbonate and copper oxide powder were used as starting materials and potassium hydroxide (KOH) was used as a solvent material. The synthesis was carried out by a heating treatment at 715°C. XRD peaks of RE124 using small ionic radius elements such as Y and Dy-Yb were obtained to be intense and sharp. The effect of RE substitution in superconductivity and lattice constant was investigated by SQUID and XRD. Superconducting critical temperature (Tc) increased and c-axis length decreased as the ion radius decreased. In order to investigate relationship between heating temperature and synthesized phases, Y124 were prepared at different heating temperature from 500°C to 800°C. Y124 phase appeared in the rage between 600°C and 800°C, and the most intense at 700°C. No Y124 phase was observed at 500°C. From these results, it was considered that small ion radius elements such as Y and Dy-Yb are appropriate to easily synthesize RE124 by this method, and the optimal heating temperature is about 700°C.