A magnetic memory element includes a laminated construction of an electrode, a first pinned layer, a first intermediate layer, a first memory layer, a second intermediate layer, a second memory layer, a third intermediate layer, a second pinned layer and electrode. The magnetization direction of the first memory layer takes a first and a second directions and that of the second memory layer takes a third and a fourth directions corresponding to a value and polarity of a current between the electrodes. In response to the current, the second intermediate layer has an electric resistance higher than the first intermediate layer and than the third intermediate layer.