  The effects of ground-state correlations on the magnetic dipole excitations
in $^{40}$Ca are studied using an extended random phase approximation (ERPA)
derived from the time-dependent density-matrix theory. Comparison is made with
other extended RPA approaches, the renormalized RPA, the self-consistent RPA
and the extended second RPA which also include the effects of ground-state
correlations. It is pointed out that direct excitations from two particle - two
hole space which are properly treated in ERPA cause strong magnetic dipole
transitions in $^{40}$Ca.
