  We show that, in the most general $N$-component theory with symmetry
O(n_1)+O(n_2), N=n_1+n_2\geq 3, the O(N)-symmetric fixed point has (at least)
three unstable directions: the temperature, the quadratic anisotropy, and the
spin-4 quartic perturbation. This implies that in the SO(5) theory of
high-$T_c$ superconductivity an additional tuning is required to obtain an
enlarged SO(5) symmetry. This is in contrast with the recent numerical results
reported by Hu, Phys. Rev. Lett. 87, 057004 (2001). \
