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The magnetic field dependence of the normal mode spectra of two-dimensional finite clusters of complex plasmas which are confined by an external harmonic potential is presented. The dependence of the normal mode spectrum as a function of a perpendicular magnetic field is discussed. The nature of the eigenmodes is investigated and the corresponding divergence and rotor were calculated which describe the "shear-like" and "compression-like" modes, respectively. It is shown that the "shear-like" character of the modes is increased due to the presence of the magnetic field.