The conditions for an almost perfect growth of smooth Cr (001) films on an iron whisker substrate have been investigated by means of reflection high energy electron diffraction (RHEED). The exchange interaction between 20 Monolayer thick Fe (001) films separated from a bulk whisker Fe (001) substrate by a variable number of Cr (001) Monolayers (ML) has been investigated by means of Brillouin light scattering experiments (BLS). These experiments show unambiguously that the exchange coupling strength between the iron film and the iron whisker can be described by a short wavelength oscillatory term superposed on a slowly varying antiferromagnetic background. The BLS data enabled one to separate the bilinear and the biquadratic contributions to the antiferromagnetic exchange coupling terms. Both the bilinear and the biquadratic coupling strengths exhibited a short period oscillatory dependence on the Cr interlayer thickness (∼2 Monolayers). Maxima in the bilinear antiferromagnetic coupling strength occur for an odd number of Cr Monolayers. This observation is not in agreement with first principles calculations. The first phase inversion has been found to occur between 4 and 5 ML of Cr.