  We give a condition under which the findings of the paper cited above work
well and determine the surfaces that were not considered before. In this paper,
we show that a parallel mean curvature surface of a general type in a complex
two-dimensional complex space form depends on one real-valued harmonic function
on the surface and five real constants if the ambient space is not flat, the
mean curvature vector does not vanish, and the Kaehler angle is not constant.
