  De Haas-van Alphen oscillations of the organic metal \k{appa}-(ET) 2 Cu(SCN)
2 have been measured up to 55 T at liquid helium temperatures. The Fermi
surface of this charge transfer salt is a textbook example of linear chain of
orbits coupled by magnetic breakdown. Accordingly, the oscillation spectrum is
composed of linear combinations of the frequencies linked to the $\alpha$ and
magnetic breakdown-induced $\beta$ orbits. The field and temperature dependence
of all the observed Fourier components, in particular the "forbidden frequency"
$\beta$ -- $\alpha$ which cannot correspond to a classical orbit, are
quantitatively accounted for by analytical calculations based on a second order
development of the free energy, i.e. beyond the first order Lifshitz-Kosevich
formula.
