An erase operation is performed on a non-volatile memory cell with an oxide-nitride-oxide structure by using a negative gate erase voltage during an erase procedure to improve the speed and performance of the non-volatile memory cell after many program-erase cycles. During the erase procedure, an erase cycle is applied followed by a read cycle until the cell has a threshold erased below a desired value. For the initial erase cycle in the procedure, an initial negative gate voltage is applied. In subsequent erase cycles, a sequentially decreasing negative gate voltage is applied until the threshold is reduced below the desired value. In one embodiment, after erase is complete, the last negative gate voltage value applied is stored in a separate memory. After a subsequent programming when the erase procedure is again applied, the initial negative gate voltage applied is the negative gate voltage value for the cell stored in memory.