Interpolation based contour metamorphosis methods often yields self-intersecting intermediate contours. In this research, we present a highly automatic algorithm to achieve non-self- intersecting contour morphing. The basic idea of our approach is to represent a planar curve with the wavelet descriptor which allows the metamorphosis at different resolutions as well as spatial locations. Furthermore, to avoid self-intersection, we formulate the mapping of control vertices of key frames as a minimization problem with a cost function involving bending and stretching of an object. Experiments of the proposed morphing algorithm are conducted to demonstrate its performance.