  We give necessary and sufficient conditions on the singular Bj\"{o}rling data
to the singular Bj\"{o}rling problem's solution has a prescribed nature of
singularity. As an application, we prove that near a maxface with a particular
type of singularity, there is another maxface having a cuspidal-edge. An
example of a maxface having various types of singularities is also given.
