  The isolated neutron star RX J0806.4-4123 was observed with XMM-Newton in
November 2000. The data from the three EPIC instruments allowed us (i) to
derive an improved X-ray position to an accuracy of 2-3'', (ii) to accumulate
the first medium-resolution soft X-ray spectra of high statistical quality and
(iii) to find a candidate for the neutron star rotation period. Although this
period of 11.3714 s is formally detected at a 3.5-\sigma level in the EPIC-pn
data, the similar pulse profiles deduced from all three EPIC instruments
increase the confidence that the period is real. The pulsed fraction of ~6%
would then be the weakest X-ray flux modulation detected from dim isolated
neutron stars. We fitted the X-ray spectra with blackbody and neutron star
atmosphere models and discuss the results with respect to the brightness limit
placed by optical images. The reduced size of the error circle on the X-ray
position should allow deeper searches for an optical counterpart.
