  One- and two-jet inclusive quantities in hadron collisions have already been
calculated to next-to-leading order accuracy, using both the subtraction and
the cone method. Since the one-loop corrections have recently been obtained for
all five-parton amplitudes, three-jet inclusive quantities can also be
predicted to next-to-leading order. The subtraction method presented in the
literature is based on a systematic use of boost-invariant kinematical
variables, and therefore its application to three-jet production is quite
cumbersome. In this paper we re-analyze the subtraction method and point out
the advantage of using angle and energy variables. This leads to simpler
results and it has complete generality, extending its validity to $n$-jet
production. The formalism is also applicable to $n$-jet production in $e^+e^-$
annihilation and in photon-hadron collisions. All the analytical results
necessary to construct an efficient numerical program for next-to-leading order
three-jet inclusive quantities in hadroproduction are given explicitly. As new
analytical result, we also report the collinear limits of all the two-to-four
processes.
