There is a hot debate about the nature of serial dependence (SD), the tendency to judge stimulus features in a given trial as similar to the previous trial. It is often argued that SD reflects a mechanism to stabilize perception, combining features of similar stimuli over time. Here, we demonstrate that SD does not combine stimulus features at all, but only task-related information. We presented a random-dot kinematogram (RDK, 1000 ms, 90% coherence, radius of 1.25°) superimposed on a noisy Gabor patch (50% of contrast, spatial frequency of 0.33 cpd, noise ratio of 40%) leading to a fused stimulus. In each trial, the tilt of the Gabor and the motion were chosen independently. We pre-cued human participants to report either one of these features. In Experiment 1, the pre-cue indicated whether the Gabor or the motion orientation should be adjusted with the mouse. In Experiment 2, we also varied the RDK speed, and the pre-cue indicated which task to perform (adjustment task on the Gabor orientation or binary speed discrimination task on the RDK). First, SD effects were identical, independent of whether the target stimulus feature was the same as in the trial before (e.g., RDK to RDK) or different (e.g., RDK to Gabor). Second, there was no SD for non-target features. Third, SD in orientation occurred only when the previous task was about orientation and not speed. These results suggest that SD is tied to task features and not to stimulus features (e.g., the ‘orientation’ independently of other elementary features). Our results do not support the notion that SD is linked to stabilizing perception.