  We study $n$-point functions at finite temperature in the closed time path
formalism. With the help of two basic column vectors and their dual partners we
derive a compact decomposition of the time-ordered $n$-point functions with
$2^n$ components in terms of $2^{n-1} -1$ independent retarded/advanced
$n$-point functions. This representation greatly simplifies calculations in the
real-time formalism.
