  In Kaszlikowski [Phys. Rev. Lett. {\bf 85}, 4418 (2000)], it has been shown
numerically that the violation of local realism for two maximally entangled
$N$-dimensional ($3 \leq N$) quantum objects is stronger than for two maximally
entangled qubits and grows with $N$. In this paper we present the analytical
proof of this fact for N=3.
