High-resolution powder neutron diffraction data have been collected at room temperature on the triclinic alpha' phase of LiZr2(PO4)(3) (HRPB, ISIS Facility, U.K.). Rietveld refinement analysis (space group C (1) over bar; Z = 4; a = 15.0718(2), b = 8.8556(1), c = 9.1233(1) Angstrom, alpha = 89.660(1), beta = 123.912(1), gamma = 90.429(1)degrees) and Fourier difference maps have revealed the presence of monoclinic pseudo-symmetry -x, y, 1/2 - z for all atoms but lithium, which is disordered over two sites Li1 and Li2 with occupancies 0.71(3) and 0.29(3), respectively. The final agreement indexes are R-p = 0.0672, wR(p) = 0.0919, R(F-2) = 0.0603 for 92 refined parameters. Both Li1 and Li2 are in distorted tetrahedral coordinations, with (Li-O) = 2.09 and 2.18 Angstrom, respectively. Pairs of centrosymmetrical Li1 sites are located within half of the available M' holes of the NASICON structure, which are split into two independent sets by triclinic breaking of symmetry. This accounts for the lower conductivity of the triclinic phase.