A phase change non-volatile memory device has a memory array with a plurality of memory cells arranged in rows and columns, a column decoder and a row decoder designed to select columns, and, respectively, rows of the memory array during operations of programming of corresponding memory cells. A control logic, coupled to the column decoder and the row decoder, is designed to execute a sequential programming command, to control the column decoder and row decoder to select one column of the memory array and execute sequential programming operations on a desired block of memory cells belonging to contiguous selected rows of the selected column.