An electrostatic precipitator for removing particulates from boiler flue gas, the electrostatic precipitator comprising: discharge electrodes and collecting electrodes fitted in a gas passage, said electrodes being arranged in at least two electrical fields that are placed successively in relation to gas flow, the electrical field establishing at least one electrical unit in transversal direction of said gas passage, the electrical unit constituting a portion of the precipitator having ability to be de-energised independently, separately from the other electrical units of the electrostatic precipitator. The first electrical field of said at last two electrical fields is arranged to be first in said gas flow. The first electrical field comprises more electrical units than a second field following said first field.