  F.~Schweiger introduced the fibred system in \cite{Schweiger-MCF}, to unify
and generalize many known continued fraction algorithms. An advantage of a
fibred system is that it often provides a systematic construction of absolutely
continuous invariant density. In this paper, we define and study the
self-duality of fibred systems, a strong symmetry of a given system. We show
that explicit algebraic self-duality holds in many systems and presents a
curious system with "partial" self-duality.
