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The magnetoimpedance effect is attractive for thin film-based magnetic sensor applications. Recently a significant progress has been made in the development of appropriate theories, preparation and characterization of MI thin film-based structures. In the present work FeNi(100 nm)/Cu(3.2 nm)]4/FeNi(100 nm)/Cu(LCu)/[FeNi(100 nm)/Cu(3.2 nm)]4/FeNi(100 nm) multilayered structures with open magnetic flux have been prepared by RF-sputtering. Their magnetic properties and MI were studied as a function of the thickness of the central Cu lead. It was shown that the thickness of the Cu lead is an important parameter. The highest sensitivity (≈ 50%/Oe, f=160 MHz) was observed for the sample with a central Cu layer thickness of about a half-thickness of a magnetic layer (LCu ≈ 250 nm). The maximum sensitivity of the real part of the impedance was also obtained for this thickness (≈ 75%/Oe).