A quasistatic unilateral contact problem with a non-local friction law is considered We propose a new variational formulation of this problem consisting of two inequalities. By applying an implicit time discretization scheme, we obtain an incremental formulation which, if the friction coefficient is sufficiently small, has a unique solution for which appropriate estimations are obtained. This incremental solution enables us to construct a solution to the quasistatic problem by establishing the weak convergence of a subsequence of mappings interpolating the incremental solution. An algorithm is derived and a simple numerical example is presented.