De Haas-van Alphen oscillations of the organic metal $theta$-(ET)$_4$ZnBr$_4$(C$_6$H$_4$Cl$_2$) are studied in pulsed magnetic fields up to 81 T. The long decay time of the pulse allows determining reliable field-dependent amplitudes of Fourier components with frequencies up to several kiloteslas. The Fourier spectrum is in agreement with the model of a linear chain of coupled orbits. In this model, all the observed frequencies are linear combinations of the frequency linked to the basic orbit $alpha$ and to the magnetic-breakdown orbit $beta$.
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