<p>The Condat–Vũ algorithm serves as a prominent primal-dual approach for addressing structured convex-concave saddle-point problems. Existing generalizations often enhance this method by incorporating relaxation strategies that extrapolate both the primal and dual variables simultaneously. In contrast, this paper proposes a novel generalization that introduces an extrapolation-correction mechanism exclusively on the dual variable. This modification preserves the simplicity and computational efficiency of the original Condat–Vũ algorithm while improving its convergence property. We prove the global convergence of the proposed algorithm under standard assumptions and derive the explicit convergence rates. Numerical experiments illustrate that our method not only accelerates convergence compared to the original Condat–Vũ algorithm but also achieves competitive performance compared to the classical relaxation-based variants.</p>