The possible formation of solitons in a Frenkel exciton system, with exciton-exciton interaction only, is studied taking into account the Pauli character of exciton operators. This is realized by choosing the trial function of the system in the form which is the particular representation of the spin coherent state for spin 1/2. Possible solutions include both `bright' and `dark' solitons. Strict conditions for the existence and stability of particular types of soliton are formulated by imposing limitations on the values of the system parameters and soliton velocity. The energy-momentum relation for both types of solution is obtained. It is concluded that neither kind of soliton can exist if the effective dynamical interaction is a repulsive one. Recent references concerning `bright' and `dark' solitons are critically assessed.