For many industrial applications, the assumption of isotropic friction is unrealistic because of directional surface machining and finishing operations. For orthotropic frictional contact, Michałowski and Mróz pointed out the non-associated nature of the sliding rule. In the present work, their law is derived from a single non-differentiable function, called a bi-potential. On this ground, the time-integration of the contact law takes the form of a predictor/corrector scheme addressing all cases (sticking, sliding, no-contact) thanks to a projection onto the friction cone. 3D numerical applications show the strong influence of the slip rule.