  We develop the Lagrangian perturbation theory in the general relativistic
cosmology, which enables us to take into account the vortical effect of the
dust matter. Under the Lagrangian representation of the fluid flow, the
propagation equation for the vorticity as well as the density is exactly
solved. Based on this, the coupling between the density and vorticity is
clarified in a non-perturbative way. The relativistic correspondence to the
Lagrangian perturbation theory in the Newtonian cosmology is also emphasized.
