Powder neutron diffraction data at high resolution (HRPD instrument, ISIS Facility, U.K.) were collected on the lithium ion conductor alpha-LiZr2(PO4)(3) at 673 K (a = 8.84448(3) Angstrom, c = 22.2875(1) Angstrom), and 873 K (a = 8.83667(4) Angstrom, c = 22.4177(2) Angstrom). Previous data measured at 423 K were included in the analysis. By Fourier maps and Rietveld refinement of the rhombohedral R (3) over barc crystal structure, it was shown that most lithium occupies the 6-fold disordered primary Li1 site, located off the symmetry center, at all temperatures. However, a 3-fold disordered secondary Li2 site was discovered, between two adjacent ZrO6 octahedra along the z axis, where a minor part of lithium is located. The fraction of lithium on Li2 increases with temperature from 10% (423 K) to 22% (873 K), and this may affect the mechanism of Li+ ion mobility. Li2 was not taken into account in the previous analysis of the 423 K data. Small but significant configurational changes of the Li1 and Li2 coordination environments occur between 423 and 873 K, which can account for the second-order phase transformation suggested in the literature to occur in the range 553 to 623 K on the basis of NMR and electrical conductivity data.