The present invention relates to magnetic or magnetoresistive random access memories (MRAMs). The present invention provides an array with magnetoresistive memory cells arranged in logically organized rows and columns, each memory cell including a magnetoresistive element (32A, 32B). The matrix comprises a set of column lines (34), a column line (34) being cells of a column. A column line (34) is shared by two adjacent columns, the shared column line (34) having an area which extends a continuous conductive strip which is magnetically couplable to the magnetoresistive element (32A, 32B) of each of the memory cells of a column. A column line (34) is shared by two adjacent columns, the shared column line (34) having an area which extends over substantially the magnetoresistive elements of the two adjacent columns sharing that column line. According to the present invention, the array furthermore comprises at least one supplementary column line (36A, 36B) per column for generating a localized magnetic field in the magnetoresistive elements (32A, 32B) of one of the adjacent columns sharing the column line (34). It is an advantage of the present invention that a higher density of the memory cells can be obtained, thus reducing space required to make a MRAM memory.