  After updating the determination of the combination of Kobayashi-Maskawa
elements $ \Im V_{td}V^*_{ts}$ according to our new estimate of the parameter
$\hat B_K$, we study the CP-violating ratio $\epsilon'/\epsilon$ by means of
hadronic matrix elements computed to $O(p^4)$ in the chiral expansion. It is
the first time that this order in chiral perturbation theory is included. We
also discuss the relevance of some $O(p^2)$ terms that are generally neglected
in the calculation of the electroweak penguin matrix elements. The most
important effect of this improved analysis is the substantial reduction (20%)
of the leading electroweak penguin matrix element and accordingly a reduced
cancelation between the electroweak and gluon penguin contributions. The ratio
$\epsilon'/\epsilon$ is thus larger than previously estimated and its predicted
value enjoys a smaller uncertainty. We find $\epsilon'/\epsilon = 1.7
^{+1.4}_{-1.0} \times 10^{-3}$. Values positive and of the order of $10^{-3}$
are therefore preferred.
