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The magnetization and magnetic-domain structure of arrays of submicrometer-size circular elements made of Fe50Pt50 films (thickness of 48 nm) have been investigated. A transition from multidomain to single-domain states with perpendicular magnetization (for ≈40% of particles) was observed as the dot diameter decreased from 550 to 200 nm. All patterned structures have hysteresis curves with a similar overall shape, both for the field applied in and out of the plane of the film. The coercivity and squareness decrease significantly with the dot size. The magnetic behavior of the elements can be explained by the partial phase transformation (face-centered cubic → face-centered tetragonal) of the initial film, as determined by X-ray diffraction.