The perovskite-like ferroelectric system PbZr1−xTixO3 (PZT) has a nearly vertical morphotropic phase boundary (MPB) around x= 0.45-0.50. Recent synchrotron x-ray powder diffraction measurements by Noheda et al. [Appl. Phys. Lett. 74, 2059(1999] have revealed a new monoclinic phase between the previously-established tetragonal and rhombohedral regions. In the present work we describe a Rietveld analysis of the detailed structure of the tetragonal and monoclinic PZT phases on a sample with x= 0.48 for which the lattice parameters are respectively: at= 4.044Å, ct= 4.138 A, at 325 K, and am= 5.721Å, bm= 5.708Å, cm= 4.138Å, β= 90.496 o , at 20K. In the tetragonal phase the shifts of the atoms along the polar [001] direction are similar to those in PbTiO3 but the refinement indicates that there are, in addition, local disordered shifts of the Pb atoms of ∼0.2Å perpendicular to the polar axis. The monoclinic structure can be viewed as a condensation along one of the 110 directions of the local displacements present in the tetragonal phase. It equally well corresponds to a freezing-out of the local displacements along one of the 100 directions recently reported by Corker et al. [J. Phys. Condens. Matter 10, 6251 (1998)] for rhombohedral PZT. The monoclinic structure therefore provides a microscopic picture of the MPB region in which one of the "locally" monoclinic phases in the "average" rhombohedral or tetragonal structures freezes out, and thus represents a bridge between these two phases. * Visiting scientist at Brookhaven National Laboratory.