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We show that an iteration of the procedure used to define the Gorenstein projective modules over a commutative ring R yields exactly the Gorenstein projective modules. Specifically, given an exact sequence of Gorenstein projective R‐modules such that the complexes Hom_R(G, H) and Hom_R(H, G) are exact for each Gorenstein projective R‐module H, the module Coker is Gorenstein projective. The proof of this result hinges upon our analysis of Gorenstein subcategories of abelian categories.