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Convex quadratic fitting (CQF) has demonstrated great success recently in the task of non-rigidly registering a face in a still image using a constrained local model (CLM). A CLM is a commonly used model for non-rigid object registration and contains two components: (i) local patch-experts that model the appearance of each landmark in the object, and (ii) a global shape prior describing how each of these landmarks can vary non-rigidly. Conventional CLMs can be used in non-rigid facial tracking applications through a track-by-detection strategy. However, the registration performance of such a strategy is susceptible to local appearance ambiguity. Since there is no motion continuity constraint between neighboring frames of the same sequence, the resultant object alignment might not be consistent from frame to frame and the motion field is not temporally smooth. In this paper, we extend the CQF fitting method into the spatio-temporal domain by enforcing the appearance consistency constraint of each local patch between neighboring frames. More importantly, we show, as in the original CQF formulation, that the global warp update can be optimized jointly in an efficient manner. Finally, we demonstrate that our approach receives improved performance for the task of non-rigid facial motion tracking on the videos of clinical patients.