Parametric active contours have been used extensively in computer vision for different tasks like segmentation and tracking. However, all parametric contours are known to suffer from the problem of frequent bunching and spacing out of curve points locally during the curve evolution. In a spline based implementation of active contours, this leads to occasional formation of loops locally, and subsequently the curve blows up due to instabilities. It has been shown earlier that in addition to usual evolution along the normal direction, the curve should also be evolved in the tangential direction for stability purposes. In this paper, we provide a mathematical basis for selecting such a suitable tangential component for stabilisation. We prove the boundedness of the evolved curve in this paper, and provide the physical significance. We demonstrate the usefulness of the proposed method with a number of experiments.