  We study one parameter deformations of a pair consisting of an analytic
singular space $X_0$ and a function $f_0$ on it, in case this defines an
isolated singularity. We prove, under general conditions, a bouquet
decomposition of the Milnor fibre when the isolated singularity splits in the
deformation and the invariance of the Milnor fibration if there is no
splitting.
