The spins of a pair of spin-orbit split surface states at a metal surface are usually antiparallelly anligned, in accord with the Rashba model for a two-dimensional electron gas. By first-principles calculations and two-photon photoemission experiments we provide evidence that in the surface alloy Bi/Cu(111) the spins of an unoccupied pair of surface states are parallelly aligned. This unconventional spin polarization, which is not consistent with that imposed by the Rashba model, is explained by hybridization of surface states with different orbital character and is attributed to the spin-orbit interaction. Since hybridization is a fundamental effect our findings are relevant for spin electroncis in general.