In this work we present an analysis of the GMI effect in FeCuNbSiB ribbons prepared by a conventional melt spinning. The samples were annealed in a magnetic field or under tensile stress using a previously nanocrystallized ribbons or combining special treatments with the crystallization. Combined with nanocrystalization field annealing of the FINEMET alloy Fe735Cu1Nb3Si13.5B9 produces almost nonhysteretic magnetoimpedance curves. In previously nanocrystallized samples field annealing can lead to higher GMI ratio, simultaneously with extremel hysteretic behaviour. Stress annealing with high specific load of 290 MPa produces the states with very complicate shape of the GMI curves including the parameters of GMI hysteresis. Maximum of ΔZ/Z ratio is obtained for the applied dc field, which overcome the anisotropy field or near the irreversibility field. The FINEMET alloy has a number of the parameters promising for the technological sensor applications.