  We present the results of an XMM-Newton observation of the slowly rotating
($P = 3.4$ s), highly magnetized ($B \approx 3 \times 10^{13}$ G) radio pulsar
PSR J0726-2612. A previous X-ray observation with the Chandra satellite showed
that some of the properties of PSR J0726-2612 are similar to those of the X-ray
Dim Isolated Neutron Stars (XDINSs), a small class of nearby slow pulsars
characterized by purely thermal X-ray spectra and undetected in the radio band.
We confirm the thermal nature of the X-ray emission of PSR J0726-2612, which
can be fit by the sum of two blackbodies with temperatures $kT_1 =
0.074_{-0.011}^{+0.006}$ keV and $kT_2 = 0.14_{-0.02}^{+0.04}$ keV and emitting
radii $R_1 = 10.4_{-2.8}^{+10.8}$ km and $R_2 = 0.5_{-0.3}^{+0.9}$ km,
respectively (assuming a distance of 1 kpc). A broad absorption line modeled
with a Gaussian profile centred at $0.39_{-0.03}^{+0.02}$ keV is required in
the fit. The pulse profile of PSR J0726-2612 is characterized by two peaks with
similar intensity separated by two unequal minima, a shape and pulsed fraction
that cannot be reproduced without invoking magnetic beaming of the X-ray
emission. The presence of a single radio pulse suggests that in PSR J0726-2612
the angles that the dipole axis and the line of sight make with the rotation
axis, $\xi$ and $\chi$ respectively, are similar. This geometry differs from
that of the two radio-silent XDINSs with a double peaked pulse profile similar
to that of PSR J0726-2612, for which $\xi \sim 90^\circ$ and $\chi \sim
45^\circ$ have been recently estimated. These results strengthen the similarity
between PSR J0726-2612 and the XDINSs and support the possibility that the lack
of radio emission from the latter might simply be due to an unfavourable
viewing geometry.
