  The production of four jets in electron-positron annihilation allows for
measuring the strong coupling and the underlying group structure of the strong
interaction simultaneously. This requires next-to-leading order perturbative
prediction for four-jet observables. In this paper we describe the theoretical
formalism of such a calculation with sufficient details. We use the dipole
method to construct a Monte Carlo program that can be used for calculating any
four-jet observable at the NLO accuracy. As new results, we present the NLO
prediction for the thrust minor, y_4 and C parameter (at C > 0.75) four-jet
shape variables and the four-jet rates with the Cambridge jet clustering
algorithm.
