There is provided an improved method for bulk (or byte) programming an array of flash EEPROM memory cells. A negative voltage is applied to the substrate of the array. A reference voltage of zero volts is applied simultaneously to the drain regions of selected memory cells that are to be programmed. There is also applied simultaneously the same reference voltage of zero volts to the control gates of the selected memory cells. The present invention provides for low current consumption and fast programming of the memory cell, which require only a single, low voltage power supply. The endurance reliability is greater than 100,000 cycles.