The perovskitelike 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 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 acid monoclinic PZT phases on a sample with x = 0.48 for which the lattice parameters are, respectively, a(1) = 4.044 Angstrom, c(t) = 4.138 Angstrom, at 325 K, and a(m) = 5.721 Angstrom, b(m) = 5.708 Angstrom, c(m) = 4.138 Angstrom, beta = 90.496 degrees, at 20 K. 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 similar to 0.2 Angstrom 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.