The structure of the ground state beyond the instability point of the quasiparticle system with a Fermi-step momentum distribution is studied within the model of a Fermi liquid with a strong repulsive interaction. A ground-state rearrangement occurs as the interaction strength is increased beyond a certain critical value. Numerical investigation of the initial stage of this structural transition shows that there are two temperature regions, corresponding to different scenarios of the rearrangement. While for temperature T larger than some characteristic temperature the behaviour of the system is the same as that in the case of fermion condensation, for an intermediate structure with a multi-connected quasiparticle momentum distribution arises.