In magnetic film memories incorporating a metal ground plate, the write noise, i.e., the sense-line voltage caused by application of the bit-current pulse, has a long "tail." By an analysis of pulse propagation along a conductor with rectangular cross section above a stratified ground plate, it is shown that 1) the slow decay of the write noise is due to current diffusion into the ground plate, and 2) the time derivative of the write noise, which should be as small as possible for best rejection by the sense system, can be considerably reduced by a) an appropriate stratification of the ground plate, and b) keeping the ground plate at a low temperature. The most effective stratified ground plate consists of a top layer of copper separated from the substrate by a layer of a ferromagnetic conductor such as Permalloy. The relative permeability of the Permalloy layer μrneed not be greater than 100. If , a Permalloy thickness of ≳ 1.5 microns makes the electrical properties of the ground plate independent of the substrate material. The optimum thickness of the copper layer is a function of the time interval between the end of the bit pulse and readout. A thick copper ground plate at liquid-nitrogen temperature is almost as effective in reducing the noise-voltage slope as the best stratified ground plate at room temperature.