We propose robust affine-invariant contour descriptor and measure for shape matching under nonlinear deformations. The descriptor is formed by orthonormal configuration matrix of local contour. The geodesic distance on Grassmann manifold is used to measure similarities of shapes under locally affine transformations, which can approximate complex deformations like articulations. A rigorous perturbation analysis proves that condition numbers of configuration matrices are critical for robustness. Then a method to improve matching stability using the condition numbers is deduced. Commonly used contour matchers, e.g., dynamical programming and others, are all applicable to the descriptor to obtain satisfied matching. Experimental evaluations are given using both synthetic and real-world images.