Most of existing works on the optimal design of balanced four-bar linkages deal essentially with the minimization of their inertia or input torques under balancing constraints. These approaches are not suitable to include constraints based on the elastic behavior of the mechanism. In order to solve this issue, we propose in this paper to perform the topology optimization of a reac-tionless four-bar linkage. Conditions for balancing the mechanism are first recalled and a topology optimization algorithm is run in order to maximize the first natural frequency while ensuring the balancing and constraining the mechanism compliance. We show that in order to obtain an interesting design solution, it is necessary to modify the balancing constraints in order to penalize them. Interesting design solutions are obtained in a rather short computational time.