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 able to be ejected, said shell being connected by a so-called rear end to a support element of the missile and being defined around a longitudinal axis called secondary longitudinal axis (L-L), said support element presenting a circular arc shape centred on the main longitudinal axis (X-X) and arranged orthogonally in relation to the latter, said support element 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 of the shell presenting a thickness (E1) adapted to said housing so as to be able to be received in said housing with a transverse contact (C1) in the bottom of the housing , a first longitudinal contact (C2) with the edge assembly and a second longitudinal contact (C3) with the crown element , said edge assembly being designed so as to enable a pivoting of the shell in relation to the body of the missile from a so-called mounting position, wherein the secondary longitudinal axis (L-L) of the shell 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 (C2) with said rear end of the shell , while the shell 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 (C2) with said rear end of the shell 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 (OXZ) containing the main longitudinal axis (X-X), each of said edge sections being designed such that the orthogonal projection thereof on said longitudinal plane (OXZ) 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 (C2) with said rear end of the shell , while the shell 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 (C2) with said rear end of the shell 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), <EOS>