  We point out a new type of diurnal effect for the cosmic ray boosted dark
matter (DM). The DM-nucleon interactions not only allow the direct detection of
DM with nuclear recoils, but also allow cosmic rays to scatter with and boost
the nonrelativistic DM to higher energies. If the DM-nuclei scattering cross
sections are sufficiently large, the DM flux is attenuated as it propagates
through the Earth, leading to a strong diurnal modulation. This diurnal
modulation provides another prominent signature for the direct detection of
boosted sub-GeV DM, in addition to signals with higher recoil energy.
