The orthorhombic compound Ba4Ru3O10 having Ru3O12 timers coupled via corner-shared oxygens in the crystal structure exhibits very interesting magnetic and transport properties. The susceptibility exhibits a broad maximum near 180K, indicating low-dimensional magnetism, followed by the AFM ordering at 105K. The neutron diffraction study shows that one of the Ru sites, Ru(2) site, orders magnetically, while another Ru site, Ru(1) site, at the centre of a trimer bears no ordered magnetic moment. This behaviour is discussed in the framework of the strong spin-orbit coupling attributed to Ru4+ (4d4 S=1) ions. The ground state of Ru(1) site is proposed to be J=0 with J=1 an excited state. It would be interesting to study the magnetic excitations, spin wave, trimers and molecular orbital excitations, using inelastic neutron scattering to understand the nature of the magnetic interactions.