The invention relates to a semiconductor memory having a multiplicity of fins made of semiconductor material which are spaced apart from one another, a multiplicity of channel regions and contact regions being formed in each of the fins, a multiplicity of word lines, a multiplicity of storage layers, at least one of the storage layers being arranged between each of the channel regions and the word line, and a multiplicity of bit lines, the longitudinal axes of first bit line portions running parallel to a first bit line direction and the longitudinal axes of second bit line portions running parallel to a second bit line direction, the second bit line direction being rotated relative to the first bit line direction, each of the bit lines being electrically connected to a multiplicity of the contact regions, wherein, between two contact regions of the same fin that are connected to one of the bit lines, a contact region is not connected to the respective bit line.