The invention relates to a Magnetic memory system (1, 20) which comprises an information layer (13) and a sensor (2, 22) for cooperating with the information layer (13). The information layer (13) comprises a pattern of magnetic bits (4a, 4b, 4c, 4d, 24a, 24c, 24d) which constitutes an array of bit locations. A bit magnetic field (3a, 3b, 3c, 3d) at a bit location represents a logical value (LO, L1/2, L1). The sensor (2, 22) comprises a magnetoresistive element (6, 26) comprising a fixed magnetic layer (7) and a free magnetic layer (8). The free magnetic layer (8) has a magnetization axis (10) along which the free magnetic layer retains a free magnetization direction (1 Ib, 1 Ic, 21b, 21c). A first bit magnetic field (3b, 3c) at one of the bit locations represents a first logical value (LO, L1/2, L1) by providing a first resistance value (Rmax, Rmid, Rmin) in the magnetoresistive element (6, 26) due to the free magnetization direction (1 Ic, 1 Ib, 21a, 21c) being substantially parallel to the magnetization axis (10). A second bit magnetic field (3a, 3d) at one of the bit locations represents a second logical value (LO, L1/2, L1) by providing a second resistance value (Rmax, Rmid, Rmin) in the magnetoresistive element (6, 26) due to the free magnetization direction (Ha, 1 Id, 21a, 2Id) having an angle (12a, 12d, 27) with the magnetization axis (10). The second bit magnetic field (3a, 3d) which provides the second resistance value (Rmax, Rmid, Rmin) is not one of the two stable magnetization directions of the free magnetic layer (8) and thus is different from the first resistance value (Rmax, Rmid, Rmin). The magnetization direction of the free magnetic layer (8) of the sensor (2, 22) no longer needs to be set before read-out.