  Linking systems are crucial for studying the homotopy theory of fusion
systems, but are also of interest from an algebraic point of view. We propose a
definition of a linking system associated to a saturated fusion system which is
more general than the one currently in the literature and thus allows a more
flexible choice of objects of linking systems. More precisely, we define
subcentric subgroups of fusion systems in a way that every quasicentric
subgroup of a saturated fusion system is subcentric. Whereas the objects of
linking systems in the current definition are always quasicentric, the objects
of our linking systems only need to be subcentric. We prove that, associated to
each saturated fusion system $\mathcal{F}$, there is a unique linking system
whose objects are the subcentric subgroups of $\mathcal{F}$. Furthermore, the
nerve of such a subcentric linking system is homotopy equivalent to the nerve
of the centric linking system associated to $\mathcal{F}$. We believe that the
existence of subcentric linking systems opens a new way for a classification of
fusion systems of characteristic $p$-type. The various results we prove about
subcentric subgroups give furthermore some evidence that the concept is of
interest for studying extensions of linking systems and fusion systems.
