During the defatting of coconut gratings from freshly harvested coconuts, the gratings are cooled to temperatures at which crystallization, i.e., solidification of the fat components occurs, before the coconut gratings are pressed. However, this temperature must not drop below the freezing point of water, preferably <2.degree. C., in order to avoid crystallization of the aqueous/liquid components of the coconut milk. As a result, the aqueous/liquid coconut milk with reduced fat content is separated from the coconut gratings in the next pressing. To separate the coconut oil from the coconut gratings, these are subsequently heated to temperatures at which the coconut oil becomes liquid in order to then separate it from the coconut gratings by pressing. The coconut oil (virgin coconut oil) is now obtained in an extremely efficient and gentle manner.