A search for the α-decay of ²³⁹Cm was carried out via the fusion reaction ²³²Th(¹²C, 5n)²³⁹Cm at GSI, applying nuclear chemistry techniques. The ²³⁹Cm α-decay would provide a link between known nuclear masses and α-decay energies measured in the region of the superheavy elements. Three different ¹²C beam energies were chosen in the present experiments. The α peaks of ^238,240Cm were observed clearly at a ¹²C energy of 74 MeV, while ²³⁸Cm disappeared at 70 MeV to provide an undisturbed α-spectrum for a sensitive search of ²³⁹Cm decay. No α-events between 6.34 and 6.50 MeV, which could be assigned to ²³⁹Cm with confidence, were observed in this experiment. The upper limit of the α-branch of ²³⁹Cm was less than 1.0 × 10^-5.