In this paper, we build the unfolding approach from acyclic sign-skew-symmetric matrices
of finite rank to skew-symmetric matrices of infinite rank, which can be regard as an improvement
of that in the skew-symmetrizable case. Using this approach, we give a positive answer
to the problem by Berenstein, Fomin and Zelevinsky in  which asks whether an acyclic signskew-
symmetric matrix is always totally sign-skew-symmetric. As applications, the positivity for
cluster algebras in acyclic sign-skew-symmetric case is given; further, the F-polynomials of cluster
algebras are proved to have constant term 1 in acyclic sign-skew-symmetric case.