  In this paper, we discuss a one parameter family of complex Born-Infeld
solitons arising from a one parameter family of minimal surfaces. The process
enables us to generate a new solution of the B-I equation from a given complex
solution of a special type (which are abundant). We illustrate this with many
examples. We find that the action or the energy of this family of solitons
remains invariant in this family and find that the well-known Lorentz symmetry
of the B-I equations is responsible for it.
