A deployment device for a fin of a projectile incorporating a hinge fixed to the projectile body which allows said fin to make a pivoting movement along at least one axis, wherein said hinge comprises a support for said fin mounted able to tilt over with respect to an axis substantially perpendicular to the projectile axis, said fin being linked to said support by a rod whose axis is substantially parallel to said projectile axis when said fin is in the folded position and substantially perpendicular to said projectile axis when said fin is in the deployed position, said rod itself being able to pivot with respect to said fin support when such said support tilts over, this pivoting of said rod being controlled by driving means.