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