Spins and parities of high spin states above the particle-binding threshold in 24Mg were determined with a basis expansion technique using triple and quadruple angular correlations between alpha particles and gamma rays. The first unambiguous identification of a 10(+) state is reported. Located at 19.2(1) MeV, this state decays predominantly by alpha emission, although a candidate gamma-decay branch with a 5.927 MeV transition connecting this 10(+) level to the rotational 8(+) state at 13.2 MeV was identified as well. The corresponding gamma-alpha branching ratio is 7(3)x10(-4).