The differential branching fraction of the decay
$\Lambda_b^0\rightarrow\Lambda\mu^+\mu^-$ is measured as a function of the
square of the dimuon invariant mass, $q^2$. A yield of $78\pm12$
$\Lambda_b^0\rightarrow\Lambda\mu^+\mu^-$ decays is observed using data,
corresponding to an integrated luminosity of 1.0\,fb$^{-1}$, collected by the
LHCb experiment at a centre-of-mass energy of 7\,TeV. A significant signal is
found in the $q^2$ region above the square of the $J/\psi$ mass, while at
lower-$q^2$ values upper limits are set on the differential branching fraction.
Integrating the differential branching fraction over $q^2$, while excluding the
$J/\psi$ and $\psi(2S)$ regions, gives a branching fraction of
$\BF($\Lambda_b^0\rightarrow\Lambda\mu^+\mu^-$)=(0.96\pm 0.16\stat\pm
0.13\syst\pm 0.21 (\mathrm{norm}))\times 10^{-6}$, where the uncertainties are
statistical, systematic and due to the normalisation mode,
$$\Lambda_b^0\rightarrow J/psi\Lambda$, respectively.
