  Faraday Rotation Measure (RM) synthesis requires the recovery of the Faraday
Dispersion Function (FDF) from measurements restricted to limited wavelength
ranges, which is an ill-conditioned deconvolution problem. Here, we propose a
novel deconvolution method based on an extension of the MUltiple SIgnal
Classification (MUSIC) algorithm. The complexity and speed of the method is
determined by the eigen-decomposition of the covariance matrix of the observed
polarizations. We show numerically that for high to moderate Signal to Noise
(S/N) cases the RM-MUSIC method is able to recover the Faraday depth values of
closely spaced pairs of thin RM components, even in situations where the peak
response of the FDF is outside of the RM range between the two input RM
components. This result is particularly important because the standard
deconvolution approach based on RM-CLEAN fails systematically in such
situations, due to its greedy mechanism used to extract the RM components. For
low S/N situations, both the RM-MUSIC and RM-CLEAN methods provide similar
results.
