  We give a maximal set of disjoint $(-1)$-sections of the well-known Lefschetz
fibration constructed by Matsumoto, Cadavid and Korkmaz. In fact, we obtain
several such sets for a fixed genus, which implies that the
Matsumoto-Cadavid-Korkmaz Lefschetz fibration has more than one supporting
minimal Lefschetz pencils. We also determine the diffeomorphism types of the
obtained supporting minimal Lefschetz pencils.
