Typically, polarization and strain in ferroelectric materials are coupled, leading to the generally accepted direct relation between polarization and unit-cell tetragonality. Here, by means of high-resolution transmission electron microscopy we map, on the unit-cell scale, the degree of tetragonality and the displacements of cations away from the centrosymmetry positions in an ultrathin epitaxial PbZr(0.2)Ti(0.8)O(3) film on a SrRuO(3) electrode layer deposited on a SrTiO(3) substrate. The lattice is highly tetragonal at the centre of the film, whereas it shows reduced tetragonality close to the interfaces. Most strikingly, we find that the maximum off-centre displacements for the central area of the film do not scale with the tetragonality. This challenges the fundamental belief in a strong polarization-tetragonality coupling in PbTiO(3)-based ferroelectrics, at such thicknesses. Furthermore, a systematic reduction of the atomic displacements is measured at the interfaces, suggesting that interface-induced suppression of the ferroelectric polarization plays a critical role in the size effect of nanoscale ferroelectrics.