  This note presents the handlebody argument for modifying achiral Lefschetz
singularities into broken Lefschetz fibrations, yielding a handlebody proof of
the existence of broken Lefschetz fibrations on arbitrary closed smooth
oriented 4-manifolds based on the earlier work of Gay and Kirby. Appeared in
Geometry and Topology 13 (2009), 312-317; the references are updated herein.
