The high temperature ferromagnetism in Sr3YCo4O 10+δ perovskite, whose origin has been the subject of a considerable debate, has been studied by neutron powder diffraction and synchrotron Xray diffraction measurements. Oxygen vacancy ordering creates a complex pattern of zigzag stripes in the oxygen-deficient CoO 4+δ layers, where the Co ions are found in three distinct coordinations. The symmetry of this unprecedented structural modulation, in conjunction with the existence of different Co spin states, provide a straightforward explanation for the appearance of ferrimagnetism. A model for the magnetic structure compatible with these structural features is proposed, based on the refinement of powder neutron data. The macroscopic moment as a function of temperature that can be calculated from the values of the ordered spins extracted from refinements, is in excellent agreement with bulk magnetization. Unlike previous models, a collinear G-type magnetic structure with uncompensated moments due to distinct spin-states of Co imposed by different coordination is found. The rich physical properties of cobalt oxides compared to other 3d transition metal oxides originate in the various electronic states of cobalt ions. Probably the first and most famous example is LaCoO 3 perovskite that undergoes a diamagnetic to paramagnetic transition on warming. The phenomenon, interpreted by Goodenough 1 as a thermally activated crossover of Co 3+ from a low-spin to a high-spin state, is due to a subtle balance between interatomic exchange energy and crystal field splitting. Nowadays many complex cobalt-oxides with fascinating electrical and magnetic properties are known, displaying superconductivity, near room-temperature giant magnetoresistance, high ionic/electronic conductivity and large thermoelectric power, making them attractive and technologically relevant.2 Practically in all cases the Co electronic configuration, primarily determined by the crystalline electric field created by first-neighbour oxygen ions, plays a central role in the underlying physics. The local Co environment is therefore a great lever to tune the electric properties and consequently the magnetic properties (spin-state) of such systems.Recently, much attention has been devoted to the oxygen-deficient perovskites Sr 3 RCo 4 O 10+δ (R=rare earth or Y) 3-6 in particular systems with oxygen content 0.5 < δ < 1 which display unconventional ferromagnetism with the highest critical temperature (T m ∼ 360K) among the known cobalt-perovskites. The basic crystal structure of Sr 3 RCo 4 O 10 of tetragonal I4/mmm symmetry, involves both cation ordering (Sr/R) and oxygen vacancy ordering with a 2a p × 2a p × 4a p superstructure with respect to the pseudo-cubic perovskite unit-cell (Fig. 1). The latter ordering produces an alternate stacking of oxygen-rich octahedral (CoO 6 ) layers and oxygendeficient tetrahedral (CoO 4 ) layers along the c-axis. For compositions with 0.5 < δ < 1, an additional superstructure has been identified (2 √ 2a p × 2 √ 2a p × 4a p ) and att...