  A transfer reaction and cluster-decay experiment,
$^{12}$C($^{16}$O,$^{24}$Mg$\rightarrow$$\alpha$+$^{20}$Ne)$\alpha$, was
performed at a beam energy of 96 MeV. Both recoil and decay $\alpha$ particles
were detected in coincidence, allowing us to deduce the energy-momentum of a
$^{20}$Ne fragment. A number of resonant states of $^{24}$Mg were reconstructed
up to an excitation energy of approximately 30 MeV. Owing to the experimentally
achieved excellent resolutions of the $Q$-value and excitation-energy spectra,
the relative decay widths for each resonant state in $^{24}$Mg to various final
states of $^{20}$Ne were extracted, alone with the total decay width. The
obtained results provide good testing ground for theoretical descriptions of
the multiple clustering configurations in $^{24}$Mg.
