Study of $Z\gamma$ Production at the Tevatron

We have studied the production of Z bosons with associated high energy photons using data collected by the CDFII detector at the Tevatron. The analysis uses the reaction $p\bar{p}$ $\to e^+ e^- \gamma$ + X at $\sqrt{s}$ = 1.96 TeV with 1 $fb^{-1}$ of integrated luminosity. Properties of these events will be discussed with an emphasis on reduction of backgrounds in the high energy photons due to hadronic jets.