The structure of the ground state beyond the instability point of the quasi
particle system with a Fermi-step momentum distribution is studied within t
he model of a Fermi liquid with a strong repulsive interaction. A ground-st
ate rearrangement occurs as the interaction strength is increased beyond a
certain critical value. Numerical investigation of the initial stage of thi
s structural transition shows that there are two temperature regions, corre
sponding to different scenarios of the rearrangement. While for temperature
T larger than some characteristic temperature To the behaviour of the syst
em is the same as that in the case of fermion condensation, for T less than
or similar to T-0 an intermediate structure with a multi-connected quasipa
rticle momentum distribution arises.