Abstract: In a cooling air passage in a gas turbine stationary blade shroud a groove at a shroud end face is formed to extend along the shroud end face. An open portion of the groove is covered by a plug so as to form a cooling air passage. A cooling air passage in which the work accuracy is remarkably enhanced can thus be very easily worked. Preferably the cooling air passage is formed by electric discharge machining (EDM). The same process can be used to form an open portion of the groove, as well as any desired turbulators. The open portion of the groove is closed by a plug which is brazed or welded in place.