The theory of generalized standard materials (GSM) is a very efficient framework to describe dissipative processes. In this framework, the behavior of the material is fully described by two convex potentials, namely the free energy and the dissipation potential. The evolution law is given by the dissipation potential, in the form of a normality rule. The framework offers several advantages, e.g. it is particularly suited for (i) deriving rigorous proofs for the existence of a solution, (ii) efficient numerical implementation with guaranteed symmetry of the stiffness matrix and (iii) combining different dissipative behaviors. Although the GSM framework encompasses a wide range of material behaviors, some dissipation laws remain incompatible with it. This is the case of the very popular Coulomb’s friction law. The incompatibility between Coulomb’s friction and GSM is a long-standing issue in theoretical mechanics and many attempts have been made to overcome this limitation over the past decades, encompassing non-local friction, a bipotential formulation, and state-dependent dissipation potentials, but none of them can reconcile standard (local) Coulomb’s friction with the GSM framework in its native form. In this work, we propose a new variational formulation of Coulomb’s friction which makes its theory (and numerical implementation) fully compatible with the GSM framework. Key to our new formulation is the introduction of a new internal variable, which is motivated by the real contact state at the microscopic level. This allows us to identify an alternative dissipation potential for Coulomb’s law. In contrast with other approaches, the contact evolution is dictated by a classical normality rule. By applying variationally consistent time integration, we derive a new incremental variational formulation for the contact problem. We implement it using standard finite elements and show examples of frictional contact between a deformable body and a rigid surface in two dimensions.