A flash memory with low power consumption and rapid operations is disclosed, including a memory array of memory cells, a word line selection circuit for selecting a row of cells, a current-type sensing circuit electrically connected with each bit line for sensing the current of a selected bit line, and an erase unit erasing the cells in a selected block of the array. The erase unit includes: an erase sequence that determines whether the current of each bit line in the erased block is larger than a first value and ends the erasure if the result is “yes”, and a soft-program sequence that performs a soft program verification, which applies a soft-program voltage to all word lines in the erased block and determines whether the current of each bit line is lower than a second value, and ends the soft programming if the result is “yes”.