A search for a neutral Higgs boson produced in association with at least one additional b quark and decaying into a pair of b quarks, is performed in a data sample corresponding to an integrated luminosity of 4.0~fb$^{-1}$, recorded by the CMS detector in proton-proton collisions at the LHC with a center-of-mass energy of 7~TeV. This search is particularly sensitive to Higgs bosons in MSSM scenarios with large values of $\tan \beta$. Upper limits on the $pp \rightarrow bH+X$, $H\rightarrow b\bar b$ cross section are derived, and interpreted in terms of bounds in the MSSM ($M_A$, $\tan\beta$) parameter space.

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