To improve uniaxial magnetic anisotropy Kugrain of c-plane-oriented columnar grains for CoCr-based perpendicular recording media, an epitaxial growth technique has been applied. The main results are as follows. (1) Using a Ru(3 nm) or Co60Cr40(20 nm)/C(1 nm) intermediate layer, Kugrain for a Co69Cr19Pt8B4 medium was enhanced from 2.04×106 erg/cm3 to 2.53×106 erg/cm3 or to 2.76×106 erg/cm3, respectively. (2) The enhancement of Kugrain depends on the composition of the magnetic layer when using the Co60Cr40/C intermediate layer. (3) The epitaxial growth technique is also effective to increase KugrainVact/kT. Especially, in the media with a high concentration of B or Cr, the thermal stability is improved mainly due to an increase of Kugrain rather than an enlargement of Vact.