Boosting to control programming of non-volatile memory

In the system for programming non-volatile storage, and provides a technique for programming with high accuracy and high speed. In one embodiment, the first voltage is applied to the first non-volatile storage element prohibits the first non-volatile storage element. The first program voltage is applied to the first non-volatile storage element. For example, a program pulse is applied to the control gate of the first non-volatile storage elements. During the program pulse, and the bit line is changed to the second voltage from the first voltage, and wherein the second voltage is such that the first non-volatile storage element is programmed.