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Heatmap regression based face alignment has achieved prominent performance on static images. However, the stability and accuracy are remarkably discounted when applying the existing methods on dynamic videos. We attribute the degradation to random noise and motion blur, which are common in videos. The temporal information is critical to address this issue yet not fully considered in the existing works. In this paper, we visit the video-oriented face alignment problem in two perspectives: detection accuracy prefers lower error for a single frame, and detection consistency forces better stability between adjacent frames. On this basis, we propose a Jitter loss function that leverages temporal information to suppress inaccurate as well as jittered landmarks. The Jitter loss is involved in a novel framework with a fine-tuning ConvLSTM structure over a backbone replaceable network. We further demonstrate that accurate and stable landmarks are associated with different regions with overlaps in a canonical coordinate, based on which the proposed Jitter loss facilitates the optimization process during training. The proposed framework achieves at least 40% improvement on stability evaluation metrics while enhancing detection accuracy versus state-of-the-art methods. Generally, it can swiftly convert a landmark detector for facial images to a better-performing one for videos without retraining the entire model.