Magnetically isotropic (CoFe-AlN)n/(AlN)n+1 multilayer films, in which the number of CoFe-AlN magnetic layers n ranged from 1 to 27, were prepared by radio frequency sputtering to achieve noise suppression at gigahertz frequencies. The soft CoFe-AlN magnetic layers consisted of nanometer-sized CoFe ferromagnetic grains embedded in an insulating AlN amorphous matrix, while the insulating AlN layers comprised AlN columnar crystals. All films showed a similar frequency dependence of permeability and ferromagnetic resonance of 1.7-GHz. Noise suppression was evaluated using a microstrip line as a noise source by determining the in-line conductive loss and the near-field intensity picked up by magnetic field detective probes. High noise suppression effects were observed in every direction in the film plane. Maximum noise suppression values amounted to 60% for the in-line conductive loss and -20-dB for the magnetic near-field intensity at around 1.7-GHz in the 27-layer film. These high-frequency noise suppression levels may be attributed to eddy current losses and ferromagnetic resonance.