  A new finite form of de Finetti's representation theorem is established using
elementary information-theoretic tools. The distribution of the first $k$
random variables in an exchangeable vector of $n\geq k$ random variables is
close to a mixture of product distributions. Closeness is measured in terms of
the relative entropy and an explicit bound is provided. This bound is tighter
than those obtained via earlier information-theoretic proofs, and its utility
extends to random variables taking values in general spaces. The core argument
employed has its origins in the quantum information-theoretic literature.
