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Recording properties of bit patterned media with weakly inclined anisotropy were studied by simulation. When a shielded planar head was used, a recording system with an areal density of 2.6 Tbit/in2 was expected for 30-degree inclined anisotropy media. Relatively large tolerance of around 4% in the anisotropy field and 7 degrees in orientation dispersion as well as write margins in down- and cross-track directions would be expected. Recording densities would be extended to 4 Tbit/in2 with additional exchange coupling between the dots. It is expected that bit patterned media with weakly inclined anisotropy is one of promising media for ultra high density recording.