Unconventional intersection designs have been used to increase the capacity of intersections that are over-saturated under conventional ones. However, existing unconventional designs typically require extra land space and their effectiveness often depends on drivers' familiarity with the uncommon operating rules. To overcome these challenges, we propose a new unconventional design, where movements that are mutually incompatible under the conventional design can be made compatible of each other by allocating exit lanes to them appropriately, thereby creating opportunities for capacity improvement. We develop a lane-based capacity optimization model that incorporates the allocation of exit lanes as decision variables. The model is formulated as a Binary Mixed Integer Linear Programming problem, which can be efficiently solved by standard branch-and-bound algorithms. Numerical experiments show that significant capacity improvement can be obtained under our design. Besides proposing a new unconventional design, we also contribute to the literature of lane-based signal optimization methods by providing a novel linear formulation for the latest, yet nonlinear, model described in Wong and Heydecker . This improvement is methodologically beneficial as linear models are computationally more convenient than nonlinear ones. Figure 8. Optimal lane configurations under the conventional design and the proposed design for cases 1 through 4. (a) Case 1: Conventional design. (b) Case 1: Proposed design. (c) Case 2: Conventional design. (d) Case 2: Proposed design. (e) Case 3: Conventional design. (f) Case 3: Proposed design. (g) Case 4: Conventional design. (h) Case 4: Proposed design.Figure 9. Signal timing plans under the conventional design and the proposed design for Cases 1 through 4. (a) Case 1: Conventional design. (b) Case 1: Proposed design. (c) Case 2: Conventional design. (d) Case 2: Proposed design. (e) Case 3: Conventional design. (f) Case 3: Proposed design. (g) Case 4: Conventional design. (h) Case 4: Proposed design.