  The LHC (CMS) discovery potential of the $e^{\pm}\mu^{\mp} + E^{miss}_T$
signature in the search for supersymmetry and lepton flavour violation in
neutralino decays is studied. A detailed study is done for the CMS test points
LM1-LM9. It is shown that for the point LM1 it is possible to detect lepton
flavour violation in neutralino decays with lepton flavour violating branching
$Br(\tilde{\chi}^0_2 \to \mu^{\pm}e^{\mp}\tilde{\chi}^0_1) \geq 0.04
Br(\tilde{\chi}^0_2 \to e^{+}e^{-}\tilde{\chi}^0_1, \mu^{+}\mu^{-}
\tilde{\chi}^0_1)$ for an integral luminosity $10 fb^{-1}$. A discovery
potential in the mSUGRA-SUSY scenario with $\tan \beta = 10, ~sign(\mu) = +$ in
the $(m_0, m_{1/2})$ plane using the $e^{\pm}\mu^{\mp} + E^{miss}_T$ signature
is determined.
