The invention relates to a method (1) for monitoring a rotating machine (100) of an aircraft, wherein a measurement signal is acquired from the rotating machine. According to the invention, instantaneous frequencies (fK(t)) of sinusoidal components of the measurement signal are estimated, and, using a computing module (12), a plurality of successive iterations are carried out in each of which: complex envelopes of the components are updated (C1), parameters of a model of a noise of the signal are updated (C21) on the basis of the envelopes, whether the model has converged from the preceding iteration to the present iteration is tested (C4), with a view to: o if not, carrying out a new iteration, o if so, performing a computation (D) of the complex envelopes on the basis of the iterations that have been carried out.