A method for writing to the magnetoresistive memory cells of a MRAM memory, includes applying write currents respectively onto a word line and a bit line. A superposition of the magnetic fields generated by the write currents in each memory cell selected by the corresponding word lines and bits lines alter a direction of the magnetization thereof. According to the method, the write currents are applied in a chronologically offset manner, to the corresponding word line and the bit line whereby the direction of magnetization of the selected memory cell is rotated in several consecutive steps in the desired direction for writing a logical "0" or "1".