The neutron-induced fission cross-section of ²⁴¹Am has been measured relative to the standard fission cross-section of ²³⁵U between 0.5 and 20MeV. The experiment was performed at the CERN n_TOF facility. Fission fragments were detected by a fast ionization chamber by discriminating against the $\alpha$ -particles from the high radioactivity of the samples. The high instantaneous neutron flux and the low background of the n_TOF facility enabled us to obtain uncertainties of $ \approx$ 5%. With the present results it was possible to resolve discrepancies between previous data sets and to confirm current evaluations, thus providing important information for design studies of future reactors with improved fuel burn-up.