  If supersymmetry is broken independently in multiple sectors with different
scales, a number of goldstinos will be generated. One linear combination of
these goldstinos is massless and eaten by the gravitino, while the orthogonal
combinations acquire a tree level mass and become the physical states named
goldstini (G'). Compared to the gravitino, such goldstini could couple more
strongly to the visible fields and lead to some exotic phenomenology. In this
note we first check the goldstini couplings in some GMSB models and find that
the goldstini-photon-neutralino interaction may be very small while the
goldstini-Z-neutralino and goldstini-Higgs-neutralino interactions may be
sizable. This can induce a new decay mode for the Higgs boson: h-> G'+\chi ->
Z+2G'. Then in an effective model with conservative fixed parameters we study
the observability of this decay channel at the LHC and find that it is not
accessible at the finished 8 TeV run (25 /fb) or 14 TeV run with 100 /fb, but
might be observed at the high luminosity LHC (14 TeV, 1000-3000 /fb) if the
systematics of the backgrounds can be well understood.
