Selective Fe₃O₄ and CuO catalysts supported on γ–χ–Al₂O₃ were successfully prepared using the facile controlled precipitation method. The catalysts Fe₃O₄/γ–χ–Al₂O₃ and CuO/γ–χ–Al₂O₃ showed excellent catalytic activity at low temperatures between 250 and 290 °C and 1 atm pressure. According to the experimental works, Fe₃O₄/γ–χ–Al₂O₃ showed better activity and selectivity at 250 °C, related to better dispersion of its active phase within the pores of γ–χ–Al₂O₃ and its lower activation energy, Ea = 46.4 kJ/mol. At 250 °C, Fe₃O₄/γ–χ–Al₂O₃ presented a higher theorical partial pressure of DME related to its better catalytic performance in the methanol dehydration reaction.