A magnetic random access memory (MRAM) has memory units or stacks of multiple memory cells arranged in the X-Y plane on the MRAM substrate with each memory unit having four possible magnetic states. Each memory unit is located at an intersection region between two orthogonal write lines and has two stacked memory cells. The two cells are magnetically separated from each other by a separation layer and have the easy axes of magnetization of their free ferromagnetic layers aligned substantially orthogonal to one another. The application of write-current pulses of equal magnitude and the appropriate direction through the orthogonal write lines above and below the memory units can generate each of the four magnetic states which can be detected as four independent logical states.