An improved synthesis is reported for N(CH3)(4)+IO4-, and its structure, low-temperature phase transition, polymorphism, and rotational disorder were studied by vibrational spectroscopy, differential scanning calorimetry, and single crystal X-ray diffraction. Its room-temperature structure (phase II) is isomorphic with N(CH3)(4)ClO4 and N(CH3)(4)BF4 and belongs to the tetragonal space group P4/nmm with Z = 2 and unit cell dimensions a 8.749(2) and c = 6.054(2) Angstrom. The structure was determined with higher precision (R = 0.036) than those of N(CH3)(4)ClO4 (R = 0.134) and N(CH3)(4)BF4 (R = 0.089) and consists of ordered N(CH3)(4)(+) cations and disordered IO4- anions which undergo free rotation about one of the I-O bonds and thereby satisfy the space group requirement for a 4-fold axis at their special (1/4, 1/4, Z) sites. As shown by its variable-temperature Raman spectra, polycrystallinic N(CH3)(4)IO4 undergoes a phase change between +10 and -10 degrees C. This phase II-phase III transition is of low energy and very broad and could not be detected by DSC. The crystal structure of phase III was determined at -30 degrees C (orthorhombic, Pbcm, Z = 4, a = 5.969(2) Angstrom, b = 12.214(3), c = 12.447(2) Angstrom, R = 0.038) and is characterized by ordered N(CH3)(4)(+) cations and ordered IO4- anions; i.e., the phase II-phase III transition involves the freezing out of the IO4- ion rotation. The vibrational spectra of phases II and III were recorded and subjected to factor group analyses. The expected high-temperature, phase II-phase I transition, presumably due to the onset of rotational disorder of the cations and found for N(CH3)(4)BF4 at 328 degrees C and N(CH3)(4)ClO4 at 340 degrees C, could not be observed for N(CH3)(4)IO4 because the latter compound explodes violently at about 247 degrees C before reaching this transition. The results of this study confirm the interpretation, proposed in 1930 by Pauling and repeatedly challenged since then, that the phase transitions in these compounds are due to the onset of ion rotation rather than positional disorder of the rotational oscillation axes.