An integrated semiconductor memory includes memory cells in a plurality of memory cell arrays disposed on a semiconductor chip in levels running above one another. A plurality of the memory cells are respectively combined to form normal units of memory cells, as well as redundant units of memory cells for replacing a respective one of the normal units. The normal units and the redundant units respectively include memory cells from memory cell arrays in a plurality of the levels. In the case of a faulty memory cell, the relevant normal unit is replaced by one of the redundant units. This permits a reduced number of programmable elements to be used for programming the redundant memory cells to repair the memory. A method for repairing such a memory is also provided.