  Unitarity cannot be perserved order by order in ordinary perturbation theory
because the constraint $UU^\dagger=\1$ is nonlinear. However, the corresponding
constraint for $K=\ln U$, being $K=-K^\dagger$, is linear so it can be
maintained in every order in a perturbative expansion of $K$. The perturbative
expansion of $K$ may be considered as a non-abelian generalization of the
linked-cluster expansion in probability theory and in statistical mechanics,
and possesses similar advantages resulting from separating the short-range
correlations from long-range effects. This point is illustrated in two QCD
examples, in which delicate cancellations encountered in summing Feynman
diagrams of are avoided when they are calculated via the perturbative expansion
of $K$. Applications to other problems are briefly discussed.
