We consider the nearest neighbor asymmetric exclusion process on ℤ, in which particles jump with probability p(1) to the right and p (-1) to the left. Let q = p(1)/p(-1) and denote by vq an ergodic component of the reversible Bernoulli product measure which places a particle at x with probability qx/(1 + qx). It is well known that under some hypotheses on a local function V, (1/√t) ∫0t V(ηs) ds converges to a normal distribution with variance σ2 = σ2(q), which depends on q. We prove in this article that σ2(q) is a C∞ function of q on (0,1). © 2005 Elsevier B. V. All rights reserved.