  We investigate the phase diagram of the Heisenberg antiferromagnet on the
square lattice with two different nearest-neighbor bonds $J$ and $J'$ ($J$-$J'$
model) at zero temperature. The model exhibits a quantum phase transition at a
critical value $J'_c > J$ between a semi-classically ordered N\'eel and a
magnetically disordered quantum paramagnetic phase of valence-bond type, which
is driven by local singlet formation on $J'$ bonds. We study the influence of
spin quantum number $s$ on this phase transition by means of a variational
mean-field approach, the coupled cluster method, and the Lanczos
exact-diagonalization technique. We present evidence that the critical value
$J'_c$ increases with growing $s$ according to $J'_c \propto s(s+1)$.
