The invention relates to a method for the oxidative dehydrogenation of ethane. The inventive method is characterized in that it consists of bringing the ethane into contact with the catalyst containing Mo, Te, V, Nb and at least a fifth element A which is selected from Cu, Ta, Sn, Se, W, Ti, Fe, Co, Ni, Cr, Zr, Sb, Bi, an alkali metal, an alkaline-earth metal and a rare earth, in which at least Mo, Te, V and Nb are present in the form of at least one oxide, said catalyst presenting, in calcined form, an X-ray diffractogram with more than ten intense diffraction lines, typically, the most intense lines corresponding to diffraction angles 2⊖ of 7.7° ±0.4, 8.9° ±0.4, 22.1° ±0.4, 26.6° ±0.4, 26.9° ±0.4, 27.1° ±0.4, 28.1° ±0.4, 31.2° ±0.4, 35.0° ±0.4 and 45.06° ±0.