The disclosure is directed to a magnetically anisotropic recording medium (2) containing a disc-shaped substrate (3) of nonmagnetic material, on the flat side (4) of which is applied a thin lower layer (8) of Si, Ge or Ti, and thereon a Co-containing alloy with vertical magnetic anisotropy. This recording medium is to assure a large signal level without the need for a special magnetically soft substrate. For this purpose, a sandwich-like multilayer structure (7) is provided according to the invention, in which at least three storage layers (10 to 13) of the Co-containing alloy with a respective thickness (d.sub.s) of at most 100 nm are separated by comparatively thinner intermediate layers (15 to 17) of the Si, Ge and/or Ti. The recording medium is advantageously provided for discs of data memories with perpendicular (vertical) magnetization.