The magnetic behaviour of the even-electron [Ni16Pd16(CO)40]4- cluster, in its [NnBu4]+ salt, has been investigated by magnetometry and muon spin rotation/relaxation (muSR) spectroscopy. The susceptibility measurements show an exceptionally high magnetic moment corresponding to a total spin value J=2. This suggests a Hund filling of a quadruplet ground state, quite unique in carbonyl-metal clusters. SQUID magnetometry shows a departure from the Curie-Weiss law, for T>150 K, and strong deviation from a Brillouin behaviour of the magnetisation curves. muSR spectroscopy in zero applied field shows a temperature independent decay of the muon spin polarisation, similar to that of a purely paramagnetic system. The observed muon spin repolarisation in a moderate external longitudinal field, however, invalidates this simple picture and suggests the presence of a local anisotropy field acting on the cluster's magnetic moment. A consistent interpretation of magnetometry and muSR results implies the occurrence of an additional interaction of the cluster spin with an effective crystalline field. The inclusion of this interaction in a model Hamiltonian allows us to successfully reproduce both the susceptibility and magnetisation data.