  The magnetic properties of the alkaline earth oxocuprate BaCu3O4 are
investigated. We show that the characteristic Cu3O4 layers of this material can
be described with diamond chains of antiferromagnetically coupled Cu 1/2 spins
with only a weak coupling between two adjacent chains. These Cu3O4 layers seem
to represent a so far unique system of weakly coupled one-dimensional magnetic
objects where the local AF ordering of the Cu2+ ions leads to an actual net
magnetic moment of an isolated diamond chain. We demonstrate a magnetic
transition at a high N\'eel temperature T_{N}=336 K.
