We report the first results from evolutions of generic black-hole binaries , i.e . a binary containing unequal mass black holes with misaligned spins . Our configuration , which has a mass ratio of 2 : 1 , consists of an initially non-spinning hole orbiting a larger , rapidly spinning hole ( specific spin a / m = 0.885 ) , with the spin direction oriented -45 ^ { \circ } with respect to the orbital plane . We track the inspiral and merger for \sim 2 orbits and find that the remnant receives a substantial kick of 454 { km s } ^ { -1 } , more than twice as large as the maximum kick from non-spinning binaries . The remnant spin direction is flipped by 103 ^ { \circ } with respect to the initial spin direction of the larger hole . We performed a second run with anti-aligned spins , a / m = \pm 0.5 lying in the orbital plane that produces a kick of \sim 1830 { km s } ^ { -1 } off the orbital plane . This value scales to nearly 4000 { km s } ^ { -1 } for maximally spinning holes . Such a large recoil velocity opens the possibility that a merged binary can be ejected even from the nucleus of a massive host galaxy .