Let X be the set of all p-centric subgroups of a finite group G and a prime p. This paper shows that the certain submodule Omega(G, x)((p)) of the Burnside ring Omega(G)((p)) of G over the localization Z((p)) of Z at p has a unique ring structure such that the mark homomorphism phi((p)) relative to x is an injective homomorphism. A key lemma of this paper is that x satisfies the condition (C)(p) that is discussed by [T. Yoshida, The generalized Burnside ring of a finite group, Hokkaido Math. J. 19 (1990) 509-574]. Diaz and Libman showed that certain ring A(p-cent)(G)((p)) is isomorphic to the Burnside ring of the fusion system associated to G and a Sylow p-subgroup in [A. Diaz, A. Libman, The Burnside ring of fusion systems, preprint, 2007]. This paper shows that A(p-cent)(G)((p)) is isomorphic to Omega(G, x)((p)). (C) 2008 Elsevier Inc. All rights reserved.