After updating the determination of the combination of Kobayashi-Maska
wa elements Im VtdVts according to our new estimate of the parameter
(B) over cap(K)$, We study the CP-violating ratio epsilon'/epsilon by
means of hadronic matrix elements computed to O(p(4)) in the chiral ex
pansion. It is the first time that this order in chiral perturbation t
heory is included. We also discuss the relevance of some O(p(2)) terms
that are generally neglected in the calculation of the electroweak pe
nguin matrix elements. The most important effect of this improved anal
ysis is the substantial reduction (20%) of the leading electroweak pen
guin matrix element and accordingly a reduced cancelation between the
electroweak and gluon penguin contributions. The ratio epsilon'/epsilo
n is thus larger than previously estimated and its predicted value enj
oys a smaller uncertainty. We find epsilon'/epsilon = 1.7(-1.0)(+1.4)
x 10(-3). Values positive and of the order of 10(-3) are therefore pre
ferred. (C) 1998 Elsevier Science B.V.