The purpose of this note is to
give a simple condition which is sufficient for a function on a real interval to be the
boundary value of a schlicht (univalent) analytic mapping of the upper half plane
into itself. This condition leads to a simple transformation which takes (possibly)
non-schlicht mappings into schlicht ones. The methods used have applications to
probability theory as well; they yield an interesting class of infinitely divisible
characteristic functions.