Predicting the future trajectories of surrounding vehicles is an important challenge in automated driving, especially in highly interactive environments such as roundabouts. Many works approach the task with behavioral cloning: A single-step prediction model is established by learning the mapping of states to the corresponding actions from a fixed dataset. To achieve a long term trajectory prediction, the single-step model is repeatedly executed. However, models learned with the behavioral cloning approach are unable to compensate for the accumulating errors that inevitably arise after repeated execution. Instead, we propose the application of multi-step learning, which directly minimizes the long term prediction error by recursively executing the model during training. This leads to a more robust and precise prediction model. The idea is showcased on a real-world dataset of more than 1000 trajectories at two roundabouts.