A search is reported for Higgs boson decay to $\mu^{+}\mu^{-}$ using data with an integrated luminosity of $24.8~\rm{fb}^{-1}$ collected with the ATLAS detector in $pp$ collisions at $\sqrt{s}$=7 and 8 TeV at the CERN Large Hadron Collider. The observed dimuon invariant mass distribution is consistent with the Standard Model background-only hypothesis in the 120-150 GeV search range. For a Higgs boson with a mass of 125.5 GeV, the observed (expected) upper limit at the 95 % confidence level is 7.0 (7.2) times the Standard Model expectation. This corresponds to an upper limit on the branching ratio BR($H \rightarrow \mu^+\mu^-$) of
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