  Generic forms of the entangled states of two spin-1 (and spin-3/2) particles,
along with the set of appropriate spin observables that together exhibit
maximum nonlocality under the Hardy's nonlocality test are given; the maximum
nonlocality is shown to be 0.09017. It is conjectured that this result holds
good for a system of two spin-$j$ particles for all values of $j$. It is also
shown that no maximally entangled state of two spin-$j$ particles responds to
the Hardy's nonlocality test.
