A plurality of turbine buckets annularly arranged around a rotor are each provided with a ledge disposed at right angles to the outer surface of each bucket. Each ledge includes a leading end portion and a trailing end portion each formed therein with a vertical hole, leading and trailing end portions of the ledge of each turbine bucket extending in opposite directions on both sides of the bucket. There are provided cover pieces each interposed between ends of the adjacent two turbine buckets and formed on the upper surface with a plurality or cylindrical projections adapted to be loosely received in the vertical holes formed in the ledges of the adjacent two turbine buckets. Contact surfaces adapted to be brought into contact with the undersides of the ledges are formed on the upper surface of each cover piece and interposed between the cylindrical projections, and an upper end portion of at least one of the cylindrical projections is machined to provide an enlarged diameter projection portion so as to preclude dislodging of the projection from the hole whereby the cover piece can positively connect the adjacent two buckets together.