  The J_1-J_2 model with the biquadratic (plaquette-four-spin) interaction was
simulated with the numerical-diagonalization method. Some limiting cases of
this model have been investigated thoroughly. Taking the advantage of the
extended parameter space, we survey the phase boundary separating the N'eel and
valence-bond-solid phases. According to the deconfined-criticality scenario,
the singularity of this phase boundary is continuous, accompanied with
unconventional critical indices. Diagonalizing the finite-size cluster with N
\le 36 spins, we observe a signature of continuous phase transition. Our
tentative estimate for the correlation-length critical exponent is \nu=1.1(3).
In order to elucidate a non-local character of criticality, we evaluated the
Roomany-Wyld \beta function around the critical point.
