Missile provided with a body presenting a longitudinal axis, called main longitudinal axis (X-X) and at least one separable nose cone, said nose cone comprising at least one shell (3, 4) able to be ejected, said shell (3, 4) being connected by a so-called rear end (3A, 4A) to a support element (11, 12) of the missile and being defined around a longitudinal axis called secondary longitudinal axis (L-L), said support element (11, 12) presenting a circular arc shape centred on the main longitudinal axis (X-X) and arranged orthogonally in relation to the latter, said support element (11, 12) being provided with an edge assembly and a crown element each presenting a circular arc shape centred on the main longitudinal axis (X-X), said crown element being arranged coaxially inside said edge assembly so as to create, between them, a housing, the rear end (3A, 4A) of the shell (3, 4) presenting a thickness adapted to said housing so as to be able to be received in said housing with a transverse contact in the bottom of the housing, a first longitudinal contact with the edge assembly and a second longitudinal contact with the crown element, said edge assembly being designed so as to enable a pivoting of the shell (3, 4) in relation to the body of the missile from a so-called mounting position, wherein the secondary longitudinal axis (L-L) of the shell (3, 4) is substantially parallel to said main longitudinal axis (X-X), towards at least one pivoted position, wherein the secondary longitudinal axis (L-L) presents a non-zero angle (α1, α2) in relation to said main longitudinal axis (X-X), said edge assembly also being designed so as to: - maintain at least partially said first longitudinal contact with said rear end (3A, 4A) of the shell (3, 4), while the shell (3, 4) has an orientation in relation to the body of the missile for which said secondary longitudinal axis (L-L) has, in relation to said main longitudinal axis (X-X) an angle smaller than a predetermined angle, called ejection angle (α0); and - end said first longitudinal contact with said rear end (3A, 4A) of the shell (3, 4) as soon as said secondary longitudinal axis (L-L) has, in relation to said main longitudinal axis (X-X), an angle higher than or equal to said ejection angle (α0), said edge assembly comprising two circular arc edge sections, arranged symmetrically in relation to a longitudinal plane containing the main longitudinal axis (X-X), each of said edge sections being designed such that the orthogonal projection thereof on said longitudinal plane presents a rectilinear front edge forming, with the rear edge thereof, an angle (β) equal to said ejection angle (α0), said rear edge being orthogonal to said main longitudinal axis (X-X). - maintain at least partially said first longitudinal contact with said rear end (3A, 4A) of the shell (3, 4), while the shell (3, 4) has an orientation in relation to the body of the missile for which said secondary longitudinal axis (L-L) has, in relation to said main longitudinal axis (X-X) an angle smaller than a predetermined angle, called ejection angle (α0); and - end said first longitudinal contact with said rear end (3A, 4A) of the shell (3, 4) as soon as said secondary longitudinal axis (L-L) has, in relation to said main longitudinal axis (X-X), an angle higher than or equal to said ejection angle (α0),