Fixing fastener with torsion bar intended to be inserted into an orifice of an element to be fixed, comprising an assembly of a body and of a core, - the body comprising: - a part for support on said element to be fixed and - a part engaging in said orifice along an axis of insertion, - the core comprising: - a torsion bar of elongate form and capable of being deformed elastically by torsion around its axis of elongation, - at least one cam surface extending around said axis of elongation and configured to co-operate with a peripheral edge of said orifice in order for the insertion of the fastener into said orifice to provoke a twisting of said bar, said at least one cam surface being linked to a relief surface configured to co-operate with said peripheral edge in order for said bar to return to a substantially strain-free position at the end of insertion of the fastener into said orifice, and of locking of the fastener with respect to said element, and - a head configured to be engaged with a torsion tool of said bar in order to displace it at least from said locking position to a position of unlocking and of removal of the fastener from said orifice, characterized in that said core is linked by a pivoting link to said body about an axis (B, D) substantially at right angles to said axis of elongation or of insertion. - the body comprising: - a part for support on said element to be fixed and - a part engaging in said orifice along an axis of insertion, - a part for support on said element to be fixed and - a part engaging in said orifice along an axis of insertion, - the core comprising: - a torsion bar of elongate form and capable of being deformed elastically by torsion around its axis of elongation, - at least one cam surface extending around said axis of elongation and configured to co-operate with a peripheral edge of said orifice in order for the insertion of the fastener into said orifice to provoke a twisting of said bar, said at least one cam surface being linked to a relief surface configured to co-operate with said peripheral edge in order for said bar to return to a substantially strain-free position at the end of insertion of the fastener into said orifice, and of locking of the fastener with respect to said element, and - a head configured to be engaged with a torsion tool of said bar in order to displace it at least from said locking position to a position of unlocking and of removal of the fastener from said orifice, - a torsion bar of elongate form and capable of being deformed elastically by torsion around its axis of elongation, - at least one cam surface extending around said axis of elongation and configured to co-operate with a peripheral edge of said orifice in order for the insertion of the fastener into said orifice to provoke a twisting of said bar, said at least one cam surface being linked to a relief surface configured to co-operate with said peripheral edge in order for said bar to return to a substantially strain-free position at the end of insertion of the fastener into said orifice, and of locking of the fastener with respect to said element, and - a head configured to be engaged with a torsion tool of said bar in order to displace it at least from said locking position to a position of unlocking and of removal of the fastener from said orifice,