Abstract: This paper presents a simple and effective method for morphing two given compatible planar triangulations with different convex boundaries. The method combines two existing algorithms and guarantees that the boundary polygons of the triangulations preserve convexity all the time during the morphing, and the intermediate triangulation at any time is compatible with the source and target triangulations, or in another word, free of self-intersection. At the same time this method realizes a convexity-preserving morph of the two convex polygons.