In this paper, the authors consider an initial boundary value problem
for the heat flow of equation of surfaces with constant mean curvatures,
which was investigated in [On the heat flow of equation of surfaces of
constant mean curvatures, Manuscripta Mathematica, 2011, 134: 259-271]
by Huang et al., where global well-posedness and finite time blow-up of
regular solutions were obtained. Their results are complemented in this
paper in the sense that some new conditions on the initial data are
provided for the solutions to develop finite time singularity.