Metal profile (2, 102, 202, 302) for a false ceiling, the metal profile including a main portion and an integral engaging member (3, 103, 203, 303) connected as a single body, or as one piece, to at least one end of the main portion, wherein said integral engaging member (3, 103, 203, 303) includes a plate-like portion and an engaging tongue or fin connected as one piece to the plate-like portion, characterized in that - said engaging tongue or fin is detached or separated from said plate-like portion on two cut sides (12,13) of said engaging tongue, - the two cut sides (12, 13) of said engaging tongue with respect to the plate-like portion are adjacent and intersecting so as to define a free angle, - the engaging tongue has one side connected to the plate-like portion, said side being a hinge side for both the cut sides (12, 13) of the engaging tongue so that the engaging tongue has a triangle shape area profile shaped like a "7": - the first cut side of said two cut sides has a first free end and a second end connected to a first end of the hinge side and the second cut side of said two cut sides is located, with respect to the first cut side, towards an inner or central zone of the metal profile and wherein the second cut side is intended to interfere with a counter-engaging edge (4, 43) of another metal profile in a engaged condition, said second cut side having a first free end defining with the first end of the first cut side said free angle and a second end forming the second end of said hinge side; - wherein said engaging tongue or fin is displaceable by means of elastic deformation between a first position in which the engaging fin is located in a rest condition protruding from a plane of the plate-like portion, and a second position in which said engaging fin is in a elastically deformed condition displaced towards the plane of the plate-like portion, and vice versa. - said engaging tongue or fin is detached or separated from said plate-like portion on two cut sides (12,13) of said engaging tongue, - the two cut sides (12, 13) of said engaging tongue with respect to the plate-like portion are adjacent and intersecting so as to define a free angle, - the engaging tongue has one side connected to the plate-like portion, said side being a hinge side for both the cut sides (12, 13) of the engaging tongue so that the engaging tongue has a triangle shape area profile shaped like a "7": - the first cut side of said two cut sides has a first free end and a second end connected to a first end of the hinge side and the second cut side of said two cut sides is located, with respect to the first cut side, towards an inner or central zone of the metal profile and wherein the second cut side is intended to interfere with a counter-engaging edge (4, 43) of another metal profile in a engaged condition, said second cut side having a first free end defining with the first end of the first cut side said free angle and a second end forming the second end of said hinge side; - wherein said engaging tongue or fin is displaceable by means of elastic deformation between a first position in which the engaging fin is located in a rest condition protruding from a plane of the plate-like portion, and a second position in which said engaging fin is in a elastically deformed condition displaced towards the plane of the plate-like portion, and vice versa. - the first cut side of said two cut sides has a first free end and a second end connected to a first end of the hinge side and the second cut side of said two cut sides is located, with respect to the first cut side, towards an inner or central zone of the metal profile and wherein the second cut side is intended to interfere with a counter-engaging edge (4, 43) of another metal profile in a engaged condition, said second cut side having a first free end defining with the first end of the first cut side said free angle and a second end forming the second end of said hinge side; - wherein said engaging tongue or fin is displaceable by means of elastic deformation between a first position in which the engaging fin is located in a rest condition protruding from a plane of the plate-like portion, and a second position in which said engaging fin is in a elastically deformed condition displaced towards the plane of the plate-like portion, and vice versa.