  It has been known for a long time that there are two non-trivial
possibilities for the relative commutation relations between a set of $m$
parafermions and a set of $n$ parabosons. These two choices are known as
``relative parafermion type'' and ``relative paraboson type'', and correspond
to quite different underlying algebraic structures. In this short note we show
how the two possibilities are related by a so-called Klein transformation.
