  We introduce a new geometric flow of Hermitian metrics which evolves an
initial metric along the second derivative of the Chern scalar curvature. The
flow depends on the choice of a background metric, it always reduces to a
scalar equation and preserves some special classes of Hermitian structures, as
balanced and Gauduchon metrics. We show that the flow has always a unique
short-time solution and we provide a stability result when the background
metric is Kaehler-Einstein with nonpositive scalar curvature.
