To image the distribution of a specific element in a specimen with an energy filtering TEM, the element-unspecific background under the core-edge has to be subtracted. The most commonly used procedure is the three-window power-law method leading to considerable systematic errors for low-energy core-edges. Here a new method is described which can be considered as a generalized difference method. Characteristic examples for element detection in biological specimens using this method are shown. The background under the core-edge can be described by one or two pre-edge windows as a polynome of third order. This function can be deduced from specimen areas that are not known to contain the element or from a second specimen used as a standard. Control experiments showed that background subtraction for on-overlapping core-edges in the low-loss region (50-200 eV) needs two pre-edge images, whereas at higher-energy losses (> 300 eV) only one pre-edge image is necessary. With the method described, objective elemental mapping becomes possible even for edges at 50-100 eV. This was proven for the M2,3-edge of iron at 60 eV. The detection of phosphorous was possible with a signal-to-noise ratio five times higher than when using the three-window method. Preliminary data showed that it should be possible to detect calcium with only one image before the edge.