A core principle of quantum theory is that nonorthogonal quantum states cannot be perfectly distinguished with single-shot measurements. However, it is possible to exclude a subset of nonorthogonal states without error in certain circumstances. Here we implement a quantum state elimination measurement which unambiguously rules out two of four pure, nonorthogonal quantum states—ideally without error and with unit success probability. This is a generalized quantum measurement with six outcomes, where each outcome corresponds to excluding a pair of states. Our experimental realization uses single photons, with information encoded in a four-dimensional state using optical path and polarization degrees of freedom. The prepared state is incorrectly ruled out up to 3.3⁢(2)% of the time.