Context. BL Lac objects show core-jet structures with features moving outwards along the jet. We present a kinematic analysis of jet component motion in the pc-scale jet of the BL Lac object S5 1803+784, which does not reveal long-term outward motion for most of the components. Aims. S5 1803+784 shows complex kinematic phenomena; understanding these provides new insights into the emission processes in BL Lac objects and possibly into the differences between quasars and BL Lac objects. Methods. The blazar S5 1803+784 has been studied with VLBI at ν = 1.6, 2. 3, 5, 8.4, and 15 GHz between 1993.88 and 2005.68 in 26 observing runs. We (re)analyzed the data and present Gaussian model-fits. We collected the already published kinematic information for this source from the literature and re-identified the components according to the new scenario presented in this paper. Altogether, 94 epochs of observations have been investigated. Results. A careful study of the long-term kinematics reveals a new picture for jet component motion in S5 1803+784. In contrast to previously discussed motion scenarios, we find that the jet structure within 12 mas of the core can most easily be described by the coexistence of several bright jet features that remain on the long-term at roughly constant core separations (in addition to the already known "stationary" jet component ∼1.4 mas) and one faint component moving with an apparent superluminal speed (∼19c, based on 3 epochs). While most of the components maintain long-term roughly constant distances from the core, we observe significant, smooth changes in their position angles. We report on an evolution of the whole jet ridge line with time over the almost 12 years of observations. The width of the jet changes periodically with a period of ∼8−9 years. We find a correlation between changes in the position angle and maxima in the total flux-density light-curves. We present evidence for a geometric origin of the observed phenomena and discuss possible models. Conclusions. We find evidence for a significantly different scenario of jet component motion in S5 1803+784 compared to the generally accepted one of outwardly moving jet components, and conclude that the observed phenomena (evolution of the jet ridge line, roughly constant component core separations but with significant position angle changes) can most easily be explained within a geometric model.