A method for working a concrete surface uses a water jet ejected from a nozzle of a nozzle holder. The nozzle holder reciprocates in cutting sweeps and moves together with a working apparatus in steps between the cutting sweeps. The water jet is directed in directions of the sweeps, and at the end of each sweep, the nozzle holder is swung into a new angle of attack for a subsequent cutting sweep. At the end of a cutting sweep, the nozzle holder begins to swing backwards simultaneously as its linear velocity increases to permit the target area to remain substantially unchanged at the start of the stepping of the working apparatus so that the water jet makes a cut forwardly in the stepping direction. The stepping and change of angle of attack are completed simultaneously immediately prior to the commencement of a subsequent cutting sweep.