  Cen X-4 is one of the best studied low-mass neutron star transients in
quiescence. Thanks to XMM-Newton large throughput, Cen X-4 was observed at the
highest signal to noise ever. This allowed us to disclose rapid (>100 s), large
(45+/-7 rms in the 10^{-4}-1 Hz range) intensity variability, especially at low
energies. In order to highlight the cause of this variability, we divided the
data into intensity intervals and fit the resulting spectra with the canonical
model for neutron star transients in quiescence, i.e. an absorbed power law
plus a neutron star atmosphere. The fit is consistent with a variable column
density plus variability in (at least) one of the spectral models. Variations
in the neutron star atmosphere might suggest that accretion onto the neutron
star surface is occuring in quiescence; variations in the power law tail should
support the view of an active millisecond radio pulsar emitting X-rays at the
shock between a radio pulsar wind and inflowing matter from the companion star.
