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Previous measurements of te magnetic susceptibility and the intensity of the 55.Mn NMR line in a number of periodic and quasiperiodic (i.e, icosahedral) Al-Mn and Al-Mn-Si alloys suggested some correlation, in that the 55.Mn line intensity decreases as the magnetic susceptibility increases. This correlation had led to the tentative conclusion that the reduction of the 55.Mn line intensity is due to the magnetism, and that the 'magnetic' Mn atoms are not seen in the NMR. We have found that the above correlation breaks down in a very susbstantial way for hexagonal Al4Mn which (i) shows a small magnetic susceptibility, and (ii) no observable 55.Mn line. Thus the reduction in intensity in the 55.Mn NMR line in the icosahedral phase is not necessarily due to its magnetism but may have its origin in another line broadening mechanism.