Full jet reconstruction in relativistic heavy ion collisions provides new and unique insights to the physics of parton energy loss. Because of the large underlying event multiplicity in $A+A$ collisions, random and correlated fluctuations in the back
ground can result in the reconstruction of fake jets. These fake jets must be identified and rejected to obtain the purest jet sample possible. A large but reducible fake rate of jets reconstructed using an iterative cone algorithm on HIJING events is observed. The absolute rate of fake jets exceeds the binary-scaled p+p jet rate below 50 GeV and is not negligible until 100 GeV. The variable $Sigma j_{T}$, the sum of the jet constituents $E_{T}$ perpendicular to the jet axis, is introduced to identify and reject fake jets at by a factor of 100 making it negligible. This variable is shown to not strongly depend on jet energy profiles modified by energy loss. By studying azimuthal correlations of reconstructed di-jets, the fake jet rate can be evaluated in data.
