Abstract: Flexible joint with two sealing lines having curvilinear portions, wherein it comprises two closed elementary joints of different length, whose axes are arranged in the same plane, joined together by a shaping template which cooperates at least with the outer joint by excrescences arranged on the outer periphery of the template and defining between them recesses at least level with the curvilinear portions of the joint, each excrescence having a groove in which is received the outer joint, each of the joints having an inner spring with contiguous turns closed on itself and at least one metal casing in which is fitted the spring.The invention more particularly relates to the construction of non-circular joints.