We discuss supersymmetry in twelve dimensions and present a covariant supersymmetric action for a brane with world-sheet signature (2,2), called a super-(2 + 2)- brane, propagating in the osp(64, 12) superspace. This superspace is explicitly constructed, and is trivial in the sense that the spinorial part is a trivial bundle over space-time, unlike the twisted superspace of usual Poincaré supersymmetry. For consistency, it is necessary to take a projection of the superspace. This is the same as the projection required for world-volume supersymmetry. Upon compactification of this superspace, a torsion is naturally introduced and we produce the membrane and type IIB string actions in eleven- and ten-dimensional Minkowski space-times. In addition, the compactification of the twelve-dimensional supersymmetry algebra produces the correct algebras for these theories, including central charges. These considerations thus give the type IIB string and M-theory a single twelve-dimensional origin.