According to one mode of implementation it is proposed to automatically accelerate the write operation by deleting on the basis of the values of the data to be written and optionally on the basis of the values of the data present in the memory the erasure step or the programming step, so doing while optionally using a conventional write command. When the memory is equipped with an error-correcting code based on a Hamming code, a property of the latter makes it possible readily to implement this possible acceleration of the cycles of writings within the memory. This property is that according to which when all the bits of the bytes of a digital word grouping together n bytes are equal to zero, the check bits associated with these bytes are also all equal to zero.