The object of the invention is a method and an arrangement for the handling of a material (1a) classified as waste that is in the flue gases (1) of a coal-fired power station, such as the handling of fly ash, in which method the fly ash (la) is separated from the flue gases (1) by means of electrostatic precipitators and is conditioned for use e.g. as an additive in the manufacture of cement, concrete, plaster and/or grouting material. In the method an electrostatic precipitator arrangement (5) comprising one or more electrostatic precipitators is used, by means of which arrangement the fly ash (la) is separated from the flue gases as more than one fraction (6a-9a), the fractions having grain sizes of different magnitudes, which fractions are conducted from the electrostatic precipitators into their own sorting hoppers for further processing.
