A process for eliminating the expandability of steel-plant slag, characterized by comprising the steps of: a) disposing the crude steel-plant slag separated by size difference and transporting it to a processing unit; b) feeding a primary crusher to reduce fragments to a grain size of smaller than 50.8 mm (2 inches), which takes place by virtue of the natural moisture of the slag, and collecting the material processed by the primary crusher; or for slag particles with a size smaller than this granulometry, diverting the material from the primary crusher; c) transporting the material from the primary crusher to a magnetic separator, in which metallic fragments bigger than a determined grain size are removed; d) drying the slag free from bigger metallic fragments in a rotary dryer; e) feeding the dry slag to an impact mill that discharges and fragments the slag to a predetermined grain size of 6.35 mm (1/4 inch); f) aero-classification with disaggregation and fragmentation that occurs in the impact mill by means of a static classifier that provides a depression inside the mill, so as to drag and collect the fine particles, being particles smaller than 100 μm and bigger than 10 μm, and superfine particles, being particles smaller than 10 μm; g) feeding slag particles bigger than 150 μm, after disaggregation and fragmentation, to a cooler, in which cooling is provided by means of an aero-classifier, which makes the heat exchange and allows the removal of the fine and superfine particles that have not been collected in the aero-classification step in the impact mill; h) disposing the cooled material on a vibrating sieve having two or more decks (23, 24, and 25) provided with screens with predetermined sizes to sieve fractions separated according to their grain sizes; i) magnetic separation of said fractions in low-intensity magnetic separators (26, 27 and 28), with generation of non-magnetic slag fractions free from metallic iron and from iron monoxide (FeO) (29, 30 and 31), and magnetic fractions (32, 33 and 34) composed by metallic iron and iron monoxide (FeO or Fe +2); and j) reprocessing said magnetic fractions (32, 33 and 34) in low-intensity magnetic separators (35, 36 and 37), with generation of concentrate with high metallic iron contents (39, 41 and 43) and a product with high concentration of iron monoxide (FeO or Fe+2) (38, 40 and 42). a) disposing the crude steel-plant slag separated by size difference and transporting it to a processing unit; b) feeding a primary crusher to reduce fragments to a grain size of smaller than 50.8 mm (2 inches), which takes place by virtue of the natural moisture of the slag, and collecting the material processed by the primary crusher; or for slag particles with a size smaller than this granulometry, diverting the material from the primary crusher; c) transporting the material from the primary crusher to a magnetic separator, in which metallic fragments bigger than a determined grain size are removed; d) drying the slag free from bigger metallic fragments in a rotary dryer; e) feeding the dry slag to an impact mill that discharges and fragments the slag to a predetermined grain size of 6.35 mm (1/4 inch); f) aero-classification with disaggregation and fragmentation that occurs in the impact mill by means of a static classifier that provides a depression inside the mill, so as to drag and collect the fine particles, being particles smaller than 100 μm and bigger than 10 μm, and superfine particles, being particles smaller than 10 μm; g) feeding slag particles bigger than 150 μm, after disaggregation and fragmentation, to a cooler, in which cooling is provided by means of an aero-classifier, which makes the heat exchange and allows the removal of the fine and superfine particles that have not been collected in the aero-classification step in the impact mill; h) disposing the cooled material on a vibrating sieve having two or more decks (23, 24, and 25) provided with screens with predetermined sizes to sieve fractions separated according to their grain sizes; i) magnetic separation of said fractions in low-intensity magnetic separators (26, 27 and 28), with generation of non-magnetic slag fractions free from metallic iron and from iron monoxide (FeO) (29, 30 and 31), and magnetic fractions (32, 33 and 34) composed by metallic iron and iron monoxide (FeO or Fe +2); and j) reprocessing said magnetic fractions (32, 33 and 34) in low-intensity magnetic separators (35, 36 and 37), with generation of concentrate with high metallic iron contents (39, 41 and 43) and a product with high concentration of iron monoxide (FeO or Fe+2) (38, 40 and 42).