Recently, Chumchob-Chen-Brito (2011) proposed the so-called mean curvature model which appeared to deliver better registration results for both smooth and non-smooth deformation fields than a large class of competing methods. However, the two displacement variables in a deformation field are regularized separately in their model and so coupling between them is not present. Therefore their mean curvature model has a weakness and may not yield the best registration results in some situations such as in non-smooth registration problems with non-axis-aligned discontinuities, as expected of a high order model. To design a new model based on interdependence between components of the deformation field, suitable for smooth and non-smooth registration problems, we propose a new vectorial curvature regularizer in this paper and present an iterative method for numerical solution of the resulting variational model. Experiments using both synthetic and realistic images confirm that the proposed model is more robust than the Chumchob-Chen-Brito (2011) model in registration quality for a wide range of examples.