  To any block idempotent $b$ of a group algebra $kG$ of a finite group $G$
over a field $k$ of characteristic $p>0$, Puig associated a fusion system and
proved that it is saturated if the $k$-algebra $kC_G(P)e$ is split, where
$(P,e)$ is a maximal $kGb$-Brauer pair. We investigate in the non-split case
how far the fusion system is from being saturated by describing it in an
explicit way as being generated by the fusion system of a related block
idempotent over a larger field together with a single automorphism of the
defect group.
