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This article is the second of a series of three presenting an alternativemethod to compute the one-loop scalar integrals. It extends the results of thefirst article to general complex masses. Let us remind the main featuresenjoyed by this method. It directly proceeds in terms of the quantities drivingalgebraic reduction methods. It applies to the four-point functions in the sameway as to the three-point functions. Lastly, it extends to kinematics moregeneral than the one of physical e.g. collider processes relevant at one loop.

A novel approach to the computation of one-loop three- and four-point functions. II - The complex mass case