In an attempt to find a material guidance to realize CoCr-based perpendicular media with high squareness and normalized coercivity, we have performed systematic magnetic characterization to examine the effects of thermal agitation and magnetic exchange interaction. The main results are as follows: (1) With decreasing measuring temperature from R. T. to 4.2 K, normalized coercivity, Hc/Hkgrain, increases for the medium strongly influenced by thermal agitation, whereas changes slightly for the medium with strong intergranular exchange coupling. (2) All the media characterized in this study have a low value of Hc/Hkgrain equal to or less than 0.36 at R. T. (3) An exchange decoupled medium (α=1.0) tends to show a large positive Hn/Hkgrain, which results in a significant decrease of loop squareness S. On the other hand, it is possible to obtain a medium with S=1 for α≫1.6 through the exchange interaction. (4) To realize a medium with S=1 and α as small as possible, selection of material with 4πMs/Hkgrain=0.2 (for α=1.6) is promising. On the other hand, to realize a medium with Hc/Hkgrain as high as possible, selection of material with 4πMs/Hkgrain=0.70 (for α=1.3) is favorable. © 2003 American Institute of Physics.