Without applying an in situ magnetic field, soft magnetic Co40Fe40B20 films were successfully deposited onto rotating silicon substrates using the oblique sputtering technique. Different thicknesses could be achieved by controlling the sputtering time. The corresponding static and dynamic electromagnetic properties were then systematically investigated. Interestingly, as the thickness increased from approximately 50 nm to 250 nm, the imaginary part of the permeability spectra of CoFeB films changed from a single peak to double peaks and then to a broad single peak. Ferromagnetic resonance (FMR), crystalline structure and cross-section SEM analyses evidenced that the double peaks of the permeability spectra are attributed to double anisotropies and anisotropic diffusion. The overlapping double FMR peaks provide a wide absorption frequency band over 2 GHz, which is critical for the design of an electromagnetic interference suppressor.