It has been proved by Herrmann, Ribbe and Schenzel that in a local ring the Gorensteiness of the associated graded ring of a power of an ideal implies the Gorensteiness of the associated graded ring of the ideal provided it is Cohen-Macaulay and the height of the ideal is at least two. We give a new proof to this theorem which covers also the height one case and so answer to a question of Herrmann, Ribbe and Schenzel whether their result holds for ideals of height one.