A new type of unstable resonator, suitable for a laser with a large medium cross section and a small or median output coupling, is presented. The resonator configuration, a modification of a negative-branch confocal unstable resonator, is numerically investigated. The basis of the theory is the Fresnel-Kirchhoff integral equation, and the calculations describe a passive resonator. With respect to output mirror tilting, the calculations confirm that the modified negative-branch confocal unstable resonator is less sensitive to mirror misalignments than the conventional negative-branch confocal unstable resonator. Furthermore, the modified resonator improves the beam quality in comparison with the conventional unstable resonator.