Chemical properties of the transactinide element, rutherfordium (Rf), produced in the reaction Cm-248(O-18,5n) have been studied at an atom-at-a-time scale. Ion-exchange experiments of Rf together with the lighter homologues in the periodic table of the elements, group-4 elements Zr and Hf, in hydrofluoric acid solutions have been conducted with a rapid ion-exchange separation apparatus. From the systematic study of the anion-exchange behavior of Rf, we have observed an unexpected chemical behavior of Rf; the fluoride complex formation of Rf is significantly different from those of the homologues. Characteristics of the complexing strength of the Rf fluoride are briefly discussed by comparing with those of Zr and Hf and also with theoretical predictions by relativistic molecular density-functional calculations.