Let f:M\rightarrow M be a C^2 diffeomorphism of a compact Riemannian manifold of dimension m\geq 2 leaving invariant an ergodic Sinai–Ruelle–Bowen measure \mu with non-zero Lyapunov exponents. We prove that \mu can be approximated by ergodic measures supported on hyperbolic horseshoes with arbitrarily large unstable dimensions.