  We propose an extension of the MSSM by adding vector like `matter' fields
with masses near the TeV scale. This extension allows us to generate the masses
of the bottom quark and tau lepton via radiative corrections such that only up
type Higgs doublet couples with quarks and leptons. In addition to providing a
natural explanation of the hierarchies between m_{b, \tau} and m_t, this new
extension, which we call FMSSM, allows the heavy sector of the MSSM Higgs
bosons to be essentially fermiophobic as well as gaugephobic. Moreover, in this
scenario there is no upper bound for the parameter \tan \beta . FMSSM can be
distinguished from the MSSM, and has peculiar and unorthodox signals at the
LHC, especially for the Higgs sector.
