Great attention has been devoted to the development of shape descriptors that is the key to object recognition. Previous works have great success on either relatively simple shapes or limited transformations, e.g., translation, rotation and scaling. We propose a new projective invariant, named characteristic number (CN) that includes more points for complex shapes with rich inner structures. Moreover, we build a novel shape descriptor with CN values calculated on triangles that cover the convex hull of a shape. The matching based on the descriptor also runs fast since only one initial point for the triangular coverage needs to align based on its CN value prior to the matching. The performance of the proposed descriptor is validated by the experiments compared with the classical shape context (SC) and recently developed cross ratio spectrum (CRS) on 32 logos of television networks with a wide range of transformations (512 images in total).