  We discuss a connection between the lantern relation in mapping class groups
and the rational blowing down process for 4-manifolds. More precisely, if we
change a positive relator in Dehn twist generators of the mapping class group
by using a lantern relation, the corresponding Lefschetz fibration changes into
its rational blowdown along a copy of the configuration C_2. We exhibit
examples of such rational blowdowns of Lefschetz fibrations whose blowup is
homeomorphic but not diffeomorphic to the original fibration.
