Multi-level programming allows for writing a first and a second bit in selected cells by separately programming the first bit from the second bit. Programming of the first bit determines a shifting from a first threshold level to a second threshold level. Programming of the second bit requires a preliminary reading to detect whether the first bit has been modified, performing a first writing step to bring the cell to a third threshold voltage if the first bit has been modified and performing a second writing step to bring the selected cell to a fourth threshold voltage different from the third threshold level if the first bit has not been modified. For increasing reading and program reliability, during preliminary reading of the second portion a reading result is forced to correspond to the first threshold level.