  The dominant decay mode of standard model Higgs at 126 GeV $b\bar{b}$ suffers
from severe SM background at the LHC even in associated productions $Wh_{\rm
SM}$ or $Z h_{\rm SM}$. The precision measurement of BR($\phi\to b\bar{b})$
requires more data to reduce its large error bar. We investigate the
possibility of this channel with largest uncertainty not dominating the decay
of Higgs-like boson discovered at the LHC. In such scenarios, the Higgs signal
shows highly suppressed $b\bar{b}$, slightly reduced $\tau^{+}\tau^{-}$ and
moderately enhanced gauge bosons comparing with the SM predictions. The model
requires two different sources of electroweak symmetry breaking and radiative
correction to $m_{b}$ strongly enhanced. However, large reduction in $b\bar{b}$
usually results large enhancement in $\tau^{+}\tau^{-}$ mode in particular. The
reduction of $\tau^{+}\tau^{-}$ therefore implies that a new decay mode is
inevitable. We find that a non-decoupling MSSM Higgs decay into lighter Higgs
$H\to hh$ may fit the signature. Here, MSSM $H$ is identified as the 126 GeV
resonance while $h$ is below $M_{H}/2$ and can evade the direct search bound at
LEPII and Tevatron. Large $PQ$ and $R$ symmetry breaking effects mediated by
strong interaction can strongly enhance radiative corrections in $m_b$.
However, the scenario can only be realized in highly fine-tuned parameter
region where $G_{Hhh}$ is tiny. Nevertheless, we discuss the discovery
potential of this highly fine-tuned $H\to hh$ at the LHC.
