  Barium ruthenate Ba$_{4}$Ru$_{3}$O$_{10}$, in which Ru$_{3}$O$_{12}$ trimers
are connected together to form a chequered two-dimensional framework, has been
synthesised and its structural, magnetic and transport properties studied
between 300 K and 2 K. The paramagnetic to antiferromagnetic transition at $T_N
\sim 105$ K evidenced on the susceptibility curve coincides with an increase of
electron localization in transport measurements. Thermoelectric power and Hall
coefficient measurements both exhibit dramatic changes at $T_N$, characteristic
of a reconstruction of the bands structure near the Fermi level. No pronounced
structural changes are observed at TN in this compound. The magnetic scattering
signal on the neutron powder diffraction patterns below $T_N$ is weak, but can
be tentatively modelled with an antiferromagnetic ordering of the spins at both
ends of a trimer, the spin of the more symmetric Ru site remaining idle.
Crystal field and strong spin-orbit coupling at the Ru$^{4+}$ site seem to be
the key parameters to understand the magnetic state of
Ba$_{4}$Ru$_{3}$O$_{10}$.
