We describe the investigation of high-spin states in 24Mg populated with the 12C(16O,α)24Mg reaction at 62- and 68-MeV beam energy. The excited states were established through the coincident detection of up to four α and γ particles in complete decay cascades toward a final state of angular momentum zero, the ground state of either 20Ne or 16O. We describe a new analysis method for the angular correlations in such events and apply it with the goal to assign spin and parity to α-unbound states in 24Mg. We establish a number of high-spin, natural-parity states between spins 6 and 12, including the lowest known 10+ and 12 + levels. The energy systematics of positive- and negative-parity high-spin states are compared to the predictions of modern shell-model calculations.