In this work the interaction of Palladium (Pd) atom with Fluorine (F) has been studied using density functional theory. Up to seven F atoms are bound to a single Pd atom which results in increase of electron affinities of given molecule successively, reaching a peak value of 8.54 eV for PdF7. By using HOMO-LUMO gap, molecular orbital analysis, binding energy of these clusters, we examined its stability and reactivity. It is found that energy required for dissociation of F2 molecules are higher than energy required for dissociation of F atoms. The unusual properties brought about by involvement of inner shell 4d-electrons, which not only allow PdFn clusters to belong to the class of superhalogens but also show that its valence can exceed the nominal value of 1.