Continuous increase in recording densities of the Co-based longitudinal media requires a drastic scaling down of the grain size in order to keep the required signal to noise ratio. However, this approach to increase the areal density will collapse when the grain size reaches the superparamagnetic limit. As an alternative, based on the analysis of the demagnetization mechanisms, Iwasaki and Takemura suggested the possibility of perpendicular magnetic recording (PMR), and computer simulation, predict areal densities of more than 300Gbit/in for this configuration. The c-axis oriented Co-based hep alloys with the magnetocrystaline anisotropy larger than the demagnetizing energy, are good candidates for the PMR media. However, before this type of materials can be realized, the magnetic domain structure must be well characterized. In this paper detailed analyses of the characteristics and shape of the magnetic domains present in the c-axis oriented CoCr films with thickness relevant for the recording industry are discussed.