We demonstrate the fractional Talbot effect of nonparaxial accelerating beams, theoretically and numerically. It is based on the interference of nonparaxial accelerating solutions of the Helmholtz equation in two dimensions. The effect originates from the interfering lobes of a superposition of the solutions that accelerate along concentric semicircular trajectories with different radii. Talbot images form along certain central angles, which are referred to as Talbot angles. The fractional nonparaxial Talbot effect is obtained by choosing the coefficients of beam components properly. A single nonparaxial accelerating beam possesses duality-it can be viewed as a Talbot effect of itself with an infinite or zero Talbot angle. These results improve the understanding of the nonparaxial accelerating beams and of the Talbot effect among them.