Abstract: A method of manufacturing a single crystal of a composite oxide by gradual solidification of a melt with solidification starting from a seed crystal which initially is in contact with the melt, is provided wherein to obtain a single crystal having a composition which is as homogeneous as possible (homogeneous within 1 mol. %) the following measures are taken: first, initially the melt consists of no more than 25% by weight of the single crystal to be grown; and second, during the solidification process molten material is added to the melt at the same rate and having the same composition as material solidifies out from the melt.