A semiconductor memory having charge trapping memory cells, where the direction of current flow of each channel region of the memory transistors runs transversely with respect to the relevant word line, the bit lines are arranged on the top side of the word lines and in a manner electrically insulated from the latter, and electrically conductive local interconnects of source-drain regions are present, which are arranged in sections in interspaces between the word lines and in a manner electrically insulated from the latter and connected to the bit lines, wherein gate electrodes are arranged in trenches at least partly formed in the memory substrate.