Jordan isomorphisms of finitary incidence algebras

Let X be a partially ordered set, R a commutative 2-torsionfree unital ring and FI(X, R) the finitary incidence algebra of X over R. In this note we prove that each R-linear Jordan isomorphism of FI(X, R) onto an R-algebra A is the near-sum of a homomorphism and an anti-homomorphism.