Lepton flavor violating (cLFV) decays of charged leptons such as $\tau to e\gamma, \tau to \mu\gamma, \mu to e\gamma$,..., are now the subjects of experiments as signals of new Physics beyond the Standard Model (SM). In the limit of the unitary gauge, we prove that contributions from one loop corrections to the above decays are very small in the framework of the economical 3-3-1 model.