Although intermediates resistance states are common in resistance random access memory (RRAM), two-way switching among them has not been demonstrated. Using a nanometallic bipolar RRAM, we have illustrated a general scheme for writing/rewriting multi-bit memory using voltage pulses. Stability conditions for accessing intermediate states have also been determined in terms of a state distribution function and the weight of serial load resistance. A multi-bit memory is shown to realize considerable space saving at a modest decrease of switching speed.