  The long baseline neutrino experiment, T2K, and the reactor experiment,
Double Chooz will soon present new data. If we expect $\sin\theta_{13}$ to be
0.1-0.2, which is close to the present experimental upper bound, we should not
persist in the paradigm of the tri-bimaximal mixing. We discuss breaking the
tri-bimaximal mixing by adding a simple mass matrix, which could be derived
from some non-Abelian discrete symmetries. It is found that
$\sin\theta_{13}=0.1-0.2$ is expected in our model independent analysis of the
generalized mass matrix for the normal or inverted hierarchical neutrino mass
spectrum. On the other hand, $\sin^2\theta_{23}$ and $\sin^2\theta_{12}$ are
expected to be not far from 1/2 and 1/3, respectively. As a typical example, we
also discuss the $A_4$ flavor model with the 1 and 1' flavons, which break the
tri-bimaximal mixing considerably. In this modified version of the Altarelli
and Feruglio model, $\sin\theta_{13}$ is predicted to be around 0.15 in the
case of the normal hierarchical neutrino masses $m_3\gg m_2, m_1$, and 0.2 in
the case of the inverted hierarchy $m_3\ll m_2, m_1$. The form of the neutrino
mass matrix looks rather interesting --- it is suggestive of other discrete
symmetries as well.
