We report on the direct observation of a large unusual antiferromagnetic exchange interaction in Fe(001) films. By measuring the magnon dispersion relation over the entire Brillouin zone of an ultrathin Fe(001) film on Rh(001), we demonstrate that the signature of this unusual antiferromagnetic exchange interaction can be observed at the high-symmetry [(M)] point. The exchange parameters are quantified by comparing the measured magnon dispersion relation with the results of our first-principles calculations. We suggest a way of examining the existence of an antiferromagnetic exchange interaction in layered magnetic structures and also a way of quantifying its strength.