Marangoni convection in a half-zone model, a simplification of the floating zone model, is steady and axisymmetric for Marangoni number Ma < Ma(c), but the azimuthal flow after instability (Ma > Ma(c)) breaks the axial-symmetry, and m-fold symmetry of the flow pattern is observed. The symmetry number m (azimuthal wave number) depends strongly on the aspect ratio, As (As = height/radius), of the half-zone. Based on the results of numerical simulation, the nature of the correlation between rn and As is investigated