The present invention concerns an electrically programmable memory and a method for writing within this memory. In order to avoid the degradation of information in a memory cell following a number of write cycles in the other cells of the same row, the present invention includes a sequence to be carried out before each write cycle of a word within a row. A systematic reading of all the words of a row by using three different read reference potentials is performed in order to find a cell that gives non-compatibility results between any two of the three read cycles. The words of the row are stored in a register. If a non-compatible result is found, which indicates a degradation of information in the row, a systematic re-write of all the words of the row is carried out.