A semiconductor memory such as a flash memory, which comprises at least one two-dimensional array of memory cells with a plurality of rows and columns of memory cells grouped in a plurality of packets. The memory cells belonging to the columns of each packet are formed in a respective semiconductor region with a first type of conductivity, this region being distinct from the semiconductor regions with the first type of conductivity in which the memory cells belonging to the columns of the remaining packets are formed. The semiconductor regions with the first type of conductivity divide the set of memory cells belonging to each row into a plurality of subsets of memory cells that constitute elemental memory units which can be modified individually. Thus memory units of very small dimensions can be erased individually, without excessive overhead in terms of area.