We present a new density functional called M06-HF. The new functional has full Hartree-Fock exchange, and therefore it eliminates self-exchange interactions at long range. This leads to good performance in TDDFT calculations of both Rydberg and charge-transfer states. In addition, the functional satisfies the uniform electron gas limit, and it is better than the popular B3LYP functional, on average, for ground-electronic-state energetics.