  Any generalized distance-squared mapping of equidimensional case has
singularities, and their singularity types are wrapped into mystery in higher
dimensional cases. Any generalized distance-squared mapping of equidimensional
case is not injective. Nevertheless, in this paper, it is shown that the
non-singular property or the injective property of a mapping is preserved by
composing a generic generalized distance-squared mapping of equidimensional
case.
